Are there specific test for various types of CPU's/memories/operating systems or there is one universal for all of them? I've heard of some programs like Prime95 and MemTest, but i don't know if they will adjust tests to different types of CPU's and memories on different types of OS (32-bit or 63-bit). Can I test both powerfull and weak machine with same test?
Prime 95 is a good cpu tester. You can use it with amd/intel processors. The maker doesn't really matter. Most people use prime 95 to test new cpus or new cooling systems for their cpus. You definitely have to monitor temps while you use a cpu stress test. You'll want to check your cpu's dangerous temp levels with the maufatcurer's site or google. Mine is 72 celius. For a good temp monitor, I recommend HWMonitor.
Memtest just tests your ram. It's a bootable file, so it will run instead of your os when your pc starts. You can put it on disc or a usb drive. I've never had problems with it. It's pretty safe.