Cheap fan usually use sleeve bearing, very simple but wear out fast if psu or ambient temp too high, the oil vaporized and the shaft will wear out causing permanent damage

A lot of casing alow us to flip the PSU, so the fan suck fresh filtered air instead of hot air inside casing.
Just need to look the air vent for PSU when buy new case.

Old one or prebiuld usually can't flip

Good PSU such as seasonic use san ace which is knowns for its quality fans, ball bearing, glass fiber blade and frame

You have few options actually
First option just install the pwm fan or 3 pin fan to your motherboard header or fan hub and the wire actually long enough exit from the original bulky wire hole then control the speed via motherboard bios or vise versa

The other options straight forward install a 2 pin fan cut off the header reused the old fan headers if needed

The other options 3 pin fan you need to loop the yellow and red together or the spinning speed just too slow, nowadays you hard to find color labeled 3 pin wire fan mostly black so you will need multi meter to test which is 5v and loop The other 2 together

2 pin red and black usually noise level quite loud

If you don't want so much hassle just do this example below

no, the psu only draw air from outside rather than hot air inside casing.
my ancient lianli and the not so new fractal design can flip PSU.
PSU never blow air into casing unless it's those HTPC.

of course dont put your PC on the floor, dust are heavy.