Aurosis

These 2 plugs are the same, just a male and female version. Historically one would go to your TV and the other to a radio. 
 
Here for internet we need to have the extra 3rd plug which has no filter on it. 
 

Right so, you're using a coaxiable broadband connection?
I do not know how these isp's work in other country's, but here in holland you can only hook 1 modem up to them, the rest are basically 'reserved' for TV only.
My home installation uses this type too, but without coax to utp converters you really can't send data over them (not that i know off anyhow). Interally we call these converters 'MOCA's'. But to be honest, if you're using existing wiring, you may just as well use powerline adapters . . . don't have much positive experiences with ethernet over coax using these types of converters.
 
But maybe a weird question . . . as your situation is rather unique and you seem to 'lack' the know how (no offense inteded), don't you perhaps have someone in your circle who can assist you with this, who can actually visit your location and give you proper advice and maybe even help you with the installation?

If you're using 2 lines, with 2 modems. with only 1 floor in between. Why not enable Wifi on those modems? Do you really need that Wifi router?
Or did you simply mean that you are buying a 2nd DECT handset, instead of a landline, and i simply misunderstood?
 
If that is the case, and you're installing your modem on the third floor. And the initial entrance of the landline is at the ground floor (1st floor for americans?), you are still needing to run a cable from the ground floor to the third floor. If this is a RJ11 connection (phone wire with 4 wires in it) and you're using it for a DSL signal, you'll likely run into interference issues, cutting down your bandwidth drastically, if even comming into a sync state at all.
 
Recommendation on DSL signals, is to keep the initial line to the modem as short as possible. Or if you have the know how, use a Cat cable to transfer the phone signal. (its shielded MUCH better). But all in all, if this is what you're doing, you could just as easily replace the phone cable for a Cat cable and run it to your computer directly, or install a switch / router / wifi acces point (acces points generally have a passthrough) on the floor your pc is on.

I think you're going a little bit overboard. But good luck!

Oef, thats a tough one, but generally no. ping is not speed related.
Ping is more related to the hardware it passes and what protocol is being used.
Ping is a representation of response time.
 
For example, UDP generally always has a lower 'ping' because it doesn't do error correction like TCP / IP does. UDP is most used in situations where it is not as critical to get every bit of information. An example of UDP is live TV. You will sometimes get artifacts because it will just discard or display the packages as they are being received (they are the digital version of white noise).
Youtube and Netflix are more like TCP/IP, where you download more into a buffer so you can do error correction and have a 'flawless' stream.
 
If you have high ping, it generally means one of the components on your route is too busy to relay the message in a timely fashion. This can mean its your pc, because you are encoding video's meanwhile or the game you're playing is bottlenecking your system. But it could also mean that because your neighbors are each downloading their full bandwidth that your share ISP network card (not to be confused with a switch like you have at home) is needing all its resources to handle the data being transferred.
 
This is not all of the story, but i think this is enough information to help you further.
 
Also, don't write off the powerline yet. It may still work, its just more likely you will run into issues. (especially if you are in an apartment complex)

Go down to your electrical panel and see what it says. Generally stuff should be somewhat labeled. For example I found me and my mom’s bedrooms are on the same 15 Amp breaker. Also consider that rules and regulations for electrical are different in each country. Here in the US most rooms are on their own breakers. That might not apply everywhere. Also it depends on when your home was built as it might still use old standards. My home was originally built in the 1930s. It has been added on over the years. We have both copper and aluminum wiring in my home. Because originally aluminum was used for electrical, then copper became the standard. 

This is a little more complicated.
Technically you can have more than 1 modem on 1 line, as that is the foundation of the PON technology (besides me as a source, here is some information on it: https://en.wikipedia.org/wiki/Passive_optical_network) and with DSL you could technically have a shared line utilizing dial in over POTS and the DSL signal, but that is far from being worth it
 
If you are located in the EU, all providers are required to support non ISP modem's, so you're always free to use your own, you will just get limited to no support from the ISP as you are not using their equipment. So in that regard donut's answer is most correct.
If and when an ISP sends you a modem, they can (and will, AVG regulated in EU ofcourse) have full control over the hardware they send you. This generally doesn't mean they will send firmware to the modem to disable it. What i think they ment to tell you is that your old modem does not support the 1gb technology that you will obtain with the new sub and as such will be disabled. Not that it won't work, but simply it won't work with the technology type of the new subscription. This in turn means you could use it as switch / router, but you don't really want to do that asyou will have limited to no control over the hardware.
 
Generally speaking, households have 1 modem for the isp part, and the more advanced users will either use a managed switch / router to connect directly to the dsl or fiber signal or hook it up behind the modem supplied by the isp. From there on creating their own private network, it being virtual or actual doesn't really matter. This is 9 out of 10 times a star model, sometimes with a router in between, but most times with switches (this later is most common as you can connect to everything in the network, where that is a little more complicated when you connect multiple subnets to eachother)  (here you have a shitty illustration ;))

For your case, the most likely is a variantion to the upper, ill illustrate with another shitty illustration

One modem per account is generally the rule. You only get 1 IP address per account unless you pay extra. 2 modems would require 2 ip addresses. Yes they can disable modems by sending out firmware that kills it or they will just block it from network access. Also if the modem came from the ISP they might want it back. 

thats one way, but honestly, cat5e will do just fine. Unless you plan on routing it alongside a 380v 'wire'?
 
But yes, best is an ethernet point to point connection from router to device.
There is real life world differences between a 1m and 25m cable, but it all depends on quality of the cable. A new cable could have been handled wrong causing quality degradation or malfunction all together. 
Theoretically 100m cable of Cat5e supports 1gbit connections. Have yet to see this amount of cable for a single run in a household tho.
Anything higher than Cat5e is better, but as you go up in numbers, the cable tends to become less and less manageable.
If you're doing this, why not go straight for a fiber connection?

Definitely an Ethernet cable. Most consistent and cheapest of the bunch.
 
Access point needs to be wired and can only transmit wifi, wlan repeater adds a bunch of latency, switch just splits Ethernet connections and powerline adapters could be good, but also bad.
 
Ethernet cable just works.

Ethernet is probably your best bet, plus a wired connection is always better at data transfers than wireless except with mice.

and there we have a limitation
It all depends on your situation really. Most homes have empty tubes running between floors specifically made for this application or more generally for electricity.
If you have empty tubes, i would utilize them, they will be the neatest way to pull the cables to the desired location.
 
If you have no such tubes, running them along the wall can be a good alternative. Maybe drill a small hole in the wall so it doesn't block the door.
The doorway is also an option, depending on how high of a clearance you have to the floor you can just run it under. If you do this, make sure the cable canot move upwards to prevent 'cutting' the cable by closing or opening the door.

wat. How is wireless better data transfer than wired with mice?

i'm not a fan of powerline adapters in all honesty. In my line of work i have seen them work awesome in the most bizarre situations, but also seen them fail in the most prestine setups, to me they are literally a wild card.
 
In theory 2000+ build should have proper wiring, and it should work if the plug connections are on the same breaker. When you have to transfer breakers you may already run into issues, and thats not everything. Basically anything connected to the same powergrid can and will cause disturbance to the signal. Dimmers are the worst, but things like flikkering lights (think about a christmas tree) are very bad too.
 
And to be honest, i think powerline adapters might be working better in third world country's, simply because they don't carry as many electrical devices on the grids

If you own the place I'd put in fixed wiring somehow. The details will depend on the house itself, how well you can hide the cabling or if you even don't care. I literally got a 30m cat5e cable (because it was cheaper than the 15m I actually needed) to replace powerline adapters as it was just too unreliable. It would randomly stop working and I'd have to go around now and then power cycling them in the hopes it comes back. However I only tried one product and it may not be representative of all of them.
 
As a 2nd choice, I'd use wifi but get your own separate AP, find an unused channel and don't let any other devices on it other than the performance sensitive ones.

My geuss is you are asking because there are some limitations to the situation, without you actually saying what they are preventing us from giving you a proper response.
People above me have stated indeed that ethernet is best. If this goes thru a switch or is a direct connection doesn't really matter. Just try to avoid having many connection points, as each of them means a loss of signal quality and thus increased ping.
 
I have drawn some arrows on your illustration which are the most logical ways to implement the cable.