I never tried overclocking anything.
The i7-7700 does not have a 'K' suffix (i.e. i7-7700K) so that rules out normal overclocking available on K-series processors that have an unlocked multiplier. Most people who want an easy time overclocking use a K-series Intel CPU, without this limitation. I'd forget any notion if overclocking a non-K CPU unless you want to complicate matters. Your non-K i7-7700 will automatically boost the frequency when appropriate. CPU-World indicates the maximum operating temperature for the i7-7700 is 100°C.
https://www.cpu-world.com/CPUs/Core_i7/Intel-Core i7 i7-7700.html
The i7-7700 has a nominal TDP rating of only 65W, which makes it easy to cool. You are unlikely to see circa 65W dissipation outside benchmarking programs such as Prime 95. Most of the time I'd expect your CPU to be dissipating significantly lower powers (a few tens of Watts).
If there's some way to tell if it's the CPU overheating,
To monitor the exact power being consumed by your CPU and measure its temperature, try Aida64 or HWMonitor. Other utilities exist.
https://www.cpuid.com/softwares/hwmonitor.html
https://www.aida64.com/downloads
I suspected the CPU to be overheating initially, but the general area around it doesn't seem to be hot at all
You're unlikely to detect high temperatures in the vicinity of a CPU, even when the internal Silicon die is running at 80 to 100°C. When I touch the heatpipes on an air cooled CPU running at well over 100W, they feel barely warm. It's the sign of a good cooler. If you were to remove the heatsink and touch the bare top of the CPU, you'd burn your finger, just before the thermal trip killed power.
I do not see anything related to PSU or CPU beyond those.
I have never seen BIOS settings relating to a PSU. Most ATX PSUs do not have control features, so there's no way for the BIOS to "adjust" the PSU's output. The PSU is a self-contained unit. It just generates power up to the point where built-in overload functions trip when a fault occurs.
As for CPU control, some BIOS have options to change maximum power/current limits on CPUs, but I leave these well alone. Similarly, you can adjust the voltage fed to the CPU, but if you get it wrong and apply too much voltage, the CPU dies. The standard CPU current/power limits do a pretty good job, unless you're going for an extreme overclock or using Liquid Nitrogen cooling, where you need more current than the standard (safe) limits allow.
The BIOS settings you've posted are merely those for fan control. I suggest enabling the warnings that inform you when the CPU fan stops working. A big air cooler heatsink will continue to protect your CPU if the fan fails, but it's a good idea to replace a faulty fan as soon as possible.
My previous CPU was Intel Pentium
The name Pentium covers hundreds of CPUs dating back decades, although most of them won't fit your motherboard. Can you tell us which model of Pentium you were using?
https://cpu-socket.com/cpu-list-lga-1151/
As already mentioned, mismatched RAM can cause instability. Until you check your RAM by booting from USB with MemTest86, we can't rule this out as the culprit. Try a matched pair, e.g. 2 x 8GB.
https://www.memtest86.com/
The thing about the RAM and Motherboard is that those issues started occurring after I got the new CPU. If it was a fault of the components I already had in, wouldn't the crashes appear earlier?
Your old Pentium might have been running your RAM at a lower frequency than your new i7-7700.
Some LGA1151 Pentiums operate down as low as DDR4-1866. The i7-7700 is rated up to DDR4-2400. If your Pentium was running at 1866MT/s and your i7-7700 is running at 2400MT/s on RAM rated a 2133MT/s, there's an obvious difference.
Are you overclocking your RAM with XMP settings. Unless you're using a matched pair of identical DIMMs, this can cause instability. Disable XMP.
