Could this also be translated as "you can read freely"? As in you can read at your own volition (in a library perhaps). Or as "You may read slowly" as in you can can read as slow as you like.
I feel like this sentence could have several different readings. ^_^
No, your sentece would be: Możesz czytać swobodnie.
Wolność - as freedom and wolno - slowly and their deratives are very similar, but in most cases they are not interchangable.
I.e. On jest wolny => He is free OR He is slow.
You could say "Wolno ci czytać" = "You are allowed to read" ("You are free to read").
To avoid the confusion between "slowly" and "freely" you could also use the word "powoli", e.g. "Wolno ci czytać powoli" = "You are allowed to read slowly" ("You are free to read slowly").
Is this a "can" of permission or of ability? Or both? "I allow you to read" or "you are able to read?"
In this example (which frankly, seems rather weird to me), I'd understand it as permission, but technically 'możesz' can mean both.
Even if it technically may be an adverb, that doesn't mean that it works in every context. In fact, out of your tries to use adjectives as adverbs, none was accepted by our native English speakers, as far as I remember. So it really doesn't seem worth trying.
Oh, of course this one also wasn't accepted.