Center speaker and AVR on same surface?

Probably not a problem. For surround systems, the distraction of video will cover any minuscule change in sound from vibration. If you want to be careful, you can put the center channel and or AVR on elastomer pucks designed to isolate them from vibration. But I doubt very much you will hear a difference even just listening to music.

It’s fine, the real issue is dealing with the bass and midrange resonances that the center will have on a shelf. If you can clean that up via manual DSP or decent speaker correction you’ll be fine. I've done this before.

Like all "bookshelf" speakers, center channels will avoid several problems on stands, but few of us have the floor space, myself included. This is why I’m using a DSP based amplifier for my new center channel project, so I can carefully tune the inevitable challenges.

The key to center speaker placement is to have the tweeters in line with the tweeters of your front L-R speakers. If you look at my system pic in my profile you can see I have the CC resting on the top of my rack. To get it inline with the L-R speakers I used a pair of Isoacoustic stands which includes 4 inch risers if you want to adjust their height. It also allows you to tilt the speakers if you want to aim it.