JoolsP

Not sure if this is any help, but that 4790k is 4/8, so it’s about the same class performance wise as a 3200g except it has worse internal graphics.  It’s old enough to be worth money though as it was the fastest cpu of that type made.  There is some serious question as to how long 4/8 will remain useful in the face of new consoles.  It is an issue the 9400f (6/6) may face as well. You might get almost as much from selling the cpu/memory as the cost of a 6/12 like a 2600/b450 system.  My personal opinion on the intel stuff offered atm is that the high thread count stuff like some i7s and i9s are the only CPUs Intel is offering atm that are likely to have long term viability.  Modern games are just getting better at using more threads, and I have a nasty suspicion they may start to require more of them as well simply through sloppy programming.

Think you should just bite the bullet and get new cpu/mobo/ram/drive.  If gaming is your cup of tea and you aren't upgrading the GPU...I'd recommend an AMD 3600, B450 mobo, 16gb of ram at 3200mhz, and a NVMe m.2 ssd.  A 9600k would make for impressive maximum frame rates, but stuttering may be noticeable...ymmv.  The perks of 12 threads on the AMD 3600 and speed of a NVMe drive is it will make for really smooth gameplay...also will function well with games that will be coming out starting 2021 me thinks.  Have to assume that because both new consoles are sporting NVMe...that all game developers are coding for said storage...taking full advantage of the >500k IOPS and >2Gbs of transfer speed.  To be clear I'm not speaking of load times, but actual in-game-processing.  New titles starting 2021...those sporting slower drives will feel it.  Below the kit costs ~$394 USD..
 

Yes, it is a very possible reason for this behaviour.
 

No it won't bottleneck a RTX 2060...or any gpu really...

I bet your board will be working much better once you repaste the chipset-cooler. Try that before buying anything new.

Nothing new supports ddr3 ram so you'll have to buy new ram anyways. It does sound like a motherboard issue to me however a 4790k is still a good cpu and I would just get a cheap z97 board and call it a day there no reason to get a super high end board really.