What are the specs of your system, and your budget ? This should help us narrow it down better
1. Fanless PSUs are usually niche items so they are mostly expensive. The good news is that if you're not gaming you'll probably need 400w at most.
The Seasonic X400 Platinum and Kingwin Stryker STR-500 would be good choices, and even the X400 Gold if you can still find one, which should be cheaper than the Platinum version.
Keep in mind you still need some airflow around it (slow case fans should suffice).
As for swapping PSU fans, I would not suggest it except a last resort measure (eg: you really like your PSU and have no budget for another one) as it can be a bit dangerous and you need to know what you're doing (knowing starting voltages for the original fan and swapped fan, risks of electrocution inside the PSU and voiding the warranty).
2. Honestly, I would not go fanless on the CPU. Going all-fanless without sufficient ventilation/surface area is a recipe for disaster, so it's usually better to have slow-spinning fans instead.
The CM Hyper 212 Shinma mentioned should be really quiet with the fan dialed down to 6-700 RPM in the BIOS controls.
Same thing with case fans: mine spins at around 650 RPM when idling or light loads and I can't hear my PC unless I'm 1 feet or so from the case.
3. Ideally, yes, to ensure a constant intake/exhaust. Is your PC a custom-built system or a Dell/HP/etc ? Most modern cases use 120mm fans, which are slower-spinning for moving the same volume of air, thus quieter... and they are the standard so they have much more variety on the market. Newer cases (like the Fractal Design R4) even come with 140mm fans now. If you can, changing the case might be a more expensive but better move overall than trying to fit quiet 80mm fans.
Additionally, if you're really interested in silent components,
Silent PC Review (SPCR) is pretty much the reference on the internet on this subject
