"Did you say "thanks" to them?"
Translation:Ĉu vi diris "dankon" al ili?
Becayse you don't use the accusative ending before a preposition, except if that preposition only indicates a place (for example, "en", which means "in/at") and you need to indicate movement ("into", for example). "Al" can already indicate movement by itself (though it doesn't necessarily always mean movement), so you'll never use the accusative before it.
No, it doesn't. You could be in the middle of a forest with nobody to hear you and still say something.
Both refer the act of talking, but the difference is the locus of attention (that is, that which you're paying attention to).
'To say' is a transitive verb, and the locus of attention is what you're saying, e.g. "I say 'hello'".
With 'to speak', the attention is on the act of talking of speaking itself, not what's being said: "I spoke at the conference". When used transitively, the locus is on the manner of speaking: "I spoke French at the conference".