What are the circular discs people use on components?

Damping plates. Several companies make them, including HRS and Artesenia. Supposed to damp resonance in the chassis. Years ago people put bricks on their components supposedly to make things sound better. Never tried them myself, so I have no opinion on their effectiveness or lack thereof.  Probably a few people around here using them, so you’ll likely get some input. 

Amazon, door weights to hold the door open

are these really necessary?

Yes. They are very necessary. Buy as many as you can afford.