Iframe set quality in url (and controls)?

All things embed are covered here

Additionally:

doesn’t support much without writing JS to control the player

and

Doesn’t let you do much either, without writing JS to control the player

So the short answer really is:

No you can’t hide the controls, as then the user won’t be able to control the video
Quality you can set with JS, but of course you have to check what qualities are valid first