Cousin has a well balanced pc.
The PSU is top quality and should be able to run any graphics card he is willing to buy.
Fast action games and higher resolutions need good graphics.
If the test above indicated that a graphics upgrade is worthwhile, that is the easiest thing to do first.
Such an upgrade is easy to move to a future cpu upgrade.
8gb ram is not usually enough.
16gb is usually plenty.
But, simply adding another 8gb is not so simple.
Ram is sold in kits for a reason.
A motherboard must manage all the ram using the same specs of voltage, cas and speed.
The internal workings are designed for the capacity of the kit.
Ram from the same vendor and part number can be made up of differing manufacturing components over time.
Some motherboards, can be very sensitive to this.
This is more difficult when more sticks are involved.
If you do buy more disparate sticks, they should be the same speed, voltage and cas numbers.
Even then your chances of working are less than 100%
I might guess 90% success .
What is your plan "B" if the new stick/s do not work?
If you want 16gb, my suggestion is to buy a 2 x 8gb kit that matches your current specs.
Then, try adding in your old 8gb,
If it works, good; you now have extra ram.
If not, sell the old ram or keep it as a spare.
The I5-7500 is an excellent processor, as far as it goes.
It will be uneconomical to buy a used i7-7700K which is the top processor that the motherboard supports. They sell for $250-$300 used on ebay.
A modern processor like the I5-10600K costs the same and is vastly stronger.
Here is a review for gaming:
https://www.tomshardware.com/reviews/intel-core-i5-10600k-cpu-review
You will need a Z490 based motherboard for best performance.
The current i5-7500 has 4 threads and a passmark rating of 6132. That is when all 4 threads are 100% utilized.
The single thread rating is 2281. That is what most games depend on.
By comparison, the i5-10600K has 12 threads and a rating of 14685/2934.
Unlike ryzen, intel does not depend on fast ram.
The current 2400 speed ram is ok.
You could start with that.
On a new build, I would go faster, in the 3200-3600 speed if the price differential is not too great.