Can I take the parts of a pre built small form factor pc and put it into a new case?

Yes, you can do all of that provided the parts you add are compatible with everything else. For example, RAM has to be the right RAM for the motherboard and for its clock setting (the speed with which it talks to the RAM). Fitting RAM that does not work at the same speed will kill its performance, not improve it. There are other ways in which RAM has to be compatible. Its best to stick to the specification of whatever is already installed, perhaps just get more of it. Most of the other peripheral parts can be slotted and and connected up provided your motherboard has the right connectors for them. The only one to look out for is the type and speed of the slot for the replacement graphics card. There's no point spending a fortune on a top rated graphics card if you can't use it to its full advantage.
When handling motherboards, RAM and the like, a sensible precaution is to wear an anti-static wrist strap, earthed/grounded to avoid zapping sensitive components.
Enjoy your build. I think you will find it easier than it seems.

For starters, there's no warranty since it's used. Second, you will encounter non-standard parts in that CPU. The arrangement from the back shows that the arrangement of parts on the motherboard is reversed. You won't be able to fit that motherboard in a standard case.

Motherboards, cases, and power supplies all come in different form factors. As long as they are all the same, there's no problem mixing parts.
An exception is the video card. If your power supply is sufficient and the motherboard and case will accept the length of your video card you should be ok.

Yes