Guilty Baby

Don't know if y'all remember but back when Intel announced these chips they had a whole section about the new chips got some new Hybrid technology that allows people to render videos while using Unreal engine at the same time. (See 8 min mark in the video.)
 
Seems like all the outlets has just forgotten about this or don't have time to test this claim. Anyone got a 13th gen CPU to test these claims?
 
Like honestly for the longest time I feel like this kind of benchmark was missing from many of the outlets (probably because they are hard to control). Like I have had so many isntances where I wanted to game while doing "work" but couldn't because my CPU sucks. Someone should test like gaming performance while rendering or compiling or even just running some code.

Do you have a bluescreen code? 

The ASUS GR8 II only has a 1060 right? I don't think you would be able to consistently hit 240Hz in moderately graphically intensive games. Unless you're willing to run on low or you're playing eSports games like LoL, CSGO and Rocket League. For games like Siege or PUBG, you'll probably get around 120 on low end settings.

Seagate Barracuda 4TB or Toshiba X300. Between the various 4TB desktop drives from the known brands, there's really not too much to distinguish any of them. 

Barring Ark, an i5 will run those games quite well, but I'd recommend an i7-7600K with a Z-board for faster memory. If you can afford an i7-7700K, go for it for the extra clocks.
Get 16GB (2x8GB) of RAM at 2800 or 3000MHz RAM. This should leave you room to expand once you find that you NEED 32GB of RAM.
I'd recommend an ultrawide 2560x1080@75Hz monitor with that 1060 6GB. Gives great gains to RTS games and 1st-person perspective games. 
I'd go ATX for expansion unless you intend to move a lot. 
Forget G-Sync and Freesync. Go for an IPS, 2560x1080@>75Hz monitor. 
PSU should be an M12ii, G2, or equivalent from the PSU Whitelist (in my sig) and Tier 4 or higher. 
For wireless, go PCIe. AC will give you some room to expand once you bring your network to AC. I like Rosewill and TP-Link WiFi cards. 
 

You can, and in theory it should go seamlessly, but in reality that's not always the case.  Up to you.
 
This is the tool if you want though https://www.easeus.com/backup-software/tb-free.html
 
You actually can clone to a smaller drive, so long as the drive is more than your total used space.

i7s are a waste of money in most games. You'll barely see a frame rate difference, some games even lose a frame or two. AMD CPUs aren't half bad right now either. You could go with the 1600.
 
ATX and ITX is just a size difference. ATX is for full towers and ITX is more like a small box. Just google ITX or ATX cases.
 
Freesync and GSync prevents a thing called screen-tearing. Plenty of images online. If it is something that bothers you go with an AMD card because Freesync monitors are cheaper. 580 for the card or something. Most people don't notice it though.
 
ARikozuM got it covered pretty good though.

Sometimes after you clone a system and use it, you'll just notice random little issues here and there - programs not working, odd bugs, etc.
@Enderman will agree

Made this one because I got bored:
It seems that your budget can get you a lot further than what you listed above
 
This is what you can get with all your budget:
 
1. So Ryzen CPUs with more cores are better than Intel i5s in those work.
 
2. A 1060 6G can easily do that. RX 570/580 prices go up and up after the mining craze, so I don't consider it atm
 
3. B boards come with M.2 slots for SSDs, More PCIe slots... Overall more features than H. For AMD, B350 allows overclock but A320 doesn't. That's why we usually avoid A320 boards.
 
4. ATX, mATX, ITX etc all refers to the size. ATX are the largest, then comes mATX, then ITX. Usually the smaller the cheaper. However, the smaller they are, the less expansion stuff they can hold, so mATX are used for most of us.
 
5. G-sync for Nvidia cards only and Freesync for AMD only. Reduces screen tearing which is covered by many websites. Screen tearing can be partly solved by enabling Vsync though, so this is not essential. G-sync monitors are very expensive, costing around 20%-30% more than non-G sync alternatives, so don't buy those unless you have some high-end Nvidia graphics card. Freesync monitors are just a little bit more expensive than those without, so I will recommend considering them if you have an edit(AMC AMD) graphics card.
 
6. IPS and TN are different types of panel on monitors. IPS give better graphical quality (especially on high-contrast graphics) and wider viewing angles than TN. They are more expensive, but I think it's worth it. If you have experienced IPS, you won't be going back to TN easily.
 
7. Check rating here first. The lower the number the tier, the better. Usually I'd say tier 3 or lower is fine, but since you have a budget like that, you should aim for tier 2 or lower.
 
8. I prefer PCIe WiFi so I don't have something hanging out of my case. Either type is fine in terms of performance though.

I converted to USD just for convenience. You can't buy jack for 750 HKD.

1.
Just OC a 1400
2.
Get an SSD if you can, if not tell him that should be his #1 priority for future upgrades
 
Other than that it looks solid for 1080p.

Get a ASUS, MSI, or Sapphire GPU, gigabyte's RX-series cooling and power delivery are subpar.
Also save up a bit more for a R5-1600 or get a 1400 and OC it, 1500X is in a weird spot.

Geogebra? It's available as a HTML5 version. 

Photoshop isn't very demanding. GPU will barely matter. Unless you have some old i3 or less than 4GB of ram it'll run fine. I use it myself on a damn MacBook Air. Rendering long GIFs might be a issue if you have 4GB of ram though. 

Photoshop isn't very demanding. GPU will barely matter. Unless you have some old i3 or less than 4GB of ram it'll run fine. I use it myself on a damn MacBook Air. Rendering long GIFs might be a issue if you have 4GB of ram though. 

Photoshop isn't very demanding. GPU will barely matter. Unless you have some old i3 or less than 4GB of ram it'll run fine. I use it myself on a damn MacBook Air. Rendering long GIFs might be a issue if you have 4GB of ram though. 

not quite.
 
 

And well the i-GPU would require a little bit more of the RAM speed. So think about it before you buy. 

http://www.newegg.com/Product/Product.aspx?Item=N82E16883800012&cm_re=compute_stick-_-83-800-012-_-Product

The Pentium has far better single threaded performance and the integrated graphics on Intel chips doesn't trail that far behind AMD APU chips. I'd get the Pentium.

Most any program will run faster on two cores that are super fast rather than four cores that are really slow. The A8 actually performs overall quite a lot worse.
http://cpu.userbenchmark.com/Compare/AMD-A8-7650K-APU-vs-Intel-Pentium-G4400/m27184vs3539
 
The multithreaded performance is barely better and the single threaded performance is where it's really, really held back.

I'd get the APU, according to Anandtech benchmarks the integrated graphics should be much more powerful (between 30-50%) than those on the pentium.
Multi threaded CPU performance should be matching on stock clockspeeds.
Single threaded performance is of course much better on the Pentium, but how many single threaded tasks are you going to be running?
 

Literally everything is hugely biased towards single threaded performance. Opening iTunes is faster on faster cores than on more cores. Opening Chrome or playing music will all work better on the Pentium. Even most of the party games OP says he/she wants to play are going to be optimized for lower-end hardware, AKA single threaded performance is all that's taken into account when programming them.

The way you explained your setup is kinda confusing. (I fully understand that English might not be your first language.)
So you have 2 SSDs and 2 HDDs.
One of the SSDs has Windows 8 on it while the other has Windows 10 on it.
Each HDD is also responsible for storing stuff for their respective OS.
So you're basically running two "virtual" computers out of one PC?
However, you did not specify where you install your programs. On the SDDs? Are the HDDs only for documents?
Do you install two copies for each software for each of the OS?
You should really unplug your Windows 8 related discs when using Windows 10.
The programs aren't meant to cross Windows version that easily.
Games from the Windows store are known not work very well and only available in Windows 10.
When upgrading from Windows 8 to Windows 10 it converts everything in all the drives to be compatible with it. That is probably why it scans your drives. Windows 10 is probably confused as to why there are still Windows 8 files around.
 
This setup doesn't make any sense and I don't get why you're doing this. You're just asking for problems. If you insist on this setup, I would advise you unplug the drives related to the other OS when booting.

Trying System File Checker right now.