High pitch noise/scratching inside the PC near CPU and RAM (coil whine?) only while gaming, no significant loss in performance

Can you record with your phone or your mic, and make a youtube video? Hard to say without actually hearing the sound.

1. Check and, if found, let the mouse out

2. Put finger on CPU cooler fan(s) and see if it stops.

3. Same with GFX card fans and case fans.

1) Coil whine has nothing to do with fans. It is resonance of electric circuits that occur within the audible human range of sufficient strength that we hear them.

They can occur in any circuit though only ones with high frequencies. Possibly the CPU voltage regulators (VRMs) if it's not the graphics card.

2) RAM stick caused freezing?
That suggest your RAM stick is either not properly inserted, or the motherboard is damaged. It's easy to confirm if the stick is properly inserted or not.

That sounds like a SEPARATE issue to me though it needs to be looked at for sure.

3) run Prime95 to stress the CPU.
The graphics card won't be stressed so if the coil whine occurs it's likely the motherboard causing it.

4) Note that COIL WHINE, especially for graphics cards varies by the type of load. So it's hard to confirm other than swapping the video card.

*If you are running say 80FPS average, try capping with VSYNC (if 60Hz monitor) or otherwise cap below the average FPS you observe to put less stress when you are hearing coil whine. It may go away as you've lowered the frequency of the components.

1. sure
2. First, I'm not clear if you now reseated the memory stick or if there's still a loose connection issue. Assuming it's NOT an issue now then the answer is that there's generally no OBVIOUS way to know if the motherboard is defective other than having problems that indicate it's the motherboard, troubleshooting (i.e. swapping parts) but the ONLY way to be certain is to swap the motherboard.

Usually if you DAMAGE the motherboard it's pretty obvious. There's no way i can think of again that you can damage the motherboard in a way that would cause coil whine.

3.
4. Uh, not sure what taking it out would accomplish. If it's a CPU related issue (i.e. VRM's) on the motherboard then a number of CPU-specific tests like Prime95 should cause the noise to occur, though again too high or too low of a load might not trigger it.

Though in P95 you can choose the number of threads to stress so try it with one, two, three and four to see if that triggers anything.

If you run games using the iGPU (inside the i5-7500) that is likely to produce a GPU bottleneck, thus load the CPU less so it's not a very useful test.

Putting that graphics card in a different system would be the best way to test, but it sounds almost CERTAIN that it's coil whine on the graphics card.

OTHER:
1) There are a few ways to address coil whine, though they may not help or may just SHIFT the coil whine to a different time:
a) change the game settings such as anti-aliasing, or
b) put an FPS cap to reduce stress on GPU (and CPU). If your monitor is 60FPS and you turn VSYNC OFF first, then tweak settings so you are on average ABOVE 60FPS, then when you turn on VSYNC it caps to 60FPS thus reducing the load on the circuits.

You can set FPS (such as NVinspector) without VSYNC. You get screen tearing but there's less lag/sluggishness.

c) underclock GPU and memory (VRAM). Try running at 80% for both just as a TEMPORARY test.

d) POSSIBLY replacing the PSU can help as it may deliver more stable voltage. If it's related to VRM's (which graphics cards have as well) it may help. No idea frankly, but in THEORY it could help.

2) Asus may actually replace the card if it's deemed to have excessive coil whine. You can contact Tech Support at least and query "can I RMA this card if coil whine is excessive?" and see what they say at least.

3) You can FIND the noise usually by rolling up some paper or use a long paper towel tube to use like a stethoscope and CAREFULLY point to different parts of the system to see where it's noisiest.