TAtari

"Ideally I would be looking for a device that takes power from a wall plug, then sends the signal over a CAT5/6 cable that i route through my unit back to my bedroom."
 
There are WiFi to Ethernet adapters like http://www.amazon.com/NETGEAR-Universal-Ethernet-Adapter-WNCE2001/dp/B003KPBRRW (first hit on google there are others)
Never tried one myself but if you have location with power and good reception to the AP where you can put a Ethernet cable to, its a better option then running long usb cables.

You can still go with the pfSense option if you have some old hardware, it doesn't need much when it comes to hardware power. I currently have Pentium G3220 and I can get that to about 12-15% (cpu usage) when pushing 900mbit+ though my wan.

One thing to bare in mind when running pfSense (or any routing software) as a vm is that patching the host can be a real pain. Since you will not have any internet access while doing it and most host systems needs to enter maintenance mode to be patched.
Other then that it works fine I was running it like that for years but I have now switched over to having a dedicated pfSense box.
 
Now on to my concerns regarding this setup:
Can someone suggest me parts for the server build! Which MB to get and which CPU and why ... 
I would go for a Workstation or Server grade ASUS board and non K rated Intel cpu. Just make sure it has the VT features enabled (most have that now a days)
Here is a good link to see what hardware is officially supported:
http://www.vmware.com/resources/compatibility/search.php?deviceCategory=io Regarding the second instance in ESXi, should I use Ubuntu or Windows Server? 
Depends on what you plan on using it for and you can run both with ease. This is the first time I'm setting up a machine with ESXi so I'm asking is it possible to make pfSense connect directly into my NIC chips?
No, you will have to use the virtual nics easiest is to use the E1000 mode then pfSense will work out of the box but you will be limited to 1gbit, to get 10gbit support you need the vmxnet3 mode but that requires that you load the drivers for them before the installation and its a bit fiddley if you don't know how bsd works. Is the idea possible? What consequences will I face? What do you guys suggest on changing?

My home 500/500 connection usually get around 800 but I guess there are some people clogging up my pipes today.

I found this to be an interesting problem so I made javascript implementation http://jsfiddle.net/g0odg633/18/ well two one fast and one visual that shows how the algorithm works...
 
You only need 1 and 0 to count all areas. You need one main loop that goes through all the items and as soon as that one finds a 0 it enters the colouring phase. The colouring phase changes all 0:s it finds to 1:s and when it cant find more 0 it exits back out to the main loop.

Then I would guess there is configuration issue on the main router/gateway unless you have the second router connected via the WAN port of it.

If you plan on coding C in the future you shouldn't start with something like Java or C# since they OO and they have automagic memory management. It would be much better just to start with C in that case. But before you chose your language think about what it is you want to create, what type of software... some languages are better suited for certain type of applications.
 
http://www.java2s.com/ great place for basic tutorials and example code its not only for Java
And if you are running windows grab the Community edition of Visual Studio http://www.visualstudio.com/ or Eclipse if you are planning of giving Java a try https://eclipse.org/

The free versions:
You use the automatic self signed coding certificate visual studio creates for you that will require the users to confirm that they should run/install the program. You create a root certificate and use that to sign your own coding certificate and use that to sign the click once installer. That way the users only need to install your root certificate once and the program will show up as signed. The other way is that you buy a coding certificate from some valid certificate vendor like https://www.digicert.com/ (223usd) or https://startssl.com/ (59usd)

My trusty old Atari 520STfm (still works)
 

My old 486SX-25 it ended up becoming a key chain (still being used as one)
Its a bit hard to read the text on it but it reads
KU80486SX-25
L3131442
SX683
INTEL(M)©1989

ClickOnce is a great way of distributing small applications if you have a website where you can host them. One thing to keep in mind is if you are using a Self Signed Coding certificate the users that installs the application will have to confirm it. And in windows 8 they made quite anoying to do so.
If its only .net dlls you can use a merger to merge the dlls with the exe, if you have none .net libs you need embed them as resources and create your own lib loader for them like the links madknight3 posted.