Where and why should I use "to" excatly? What does "to" mean actually? Isn't it means "this" or "this is"?
It's sort of like then - when I sleep, (then) I don't talk
if you want, then come = jeśli chcesz, to przyjdź
I guess it's unclear to me in two sentences that mean the same thing, why there would be two verbs with the same meaning, yet each would require a different declension on the object
Why does the TTS pronounciation change when it speaks the full sentence compared to single words
That's how TTS works. The slower the pronunciation, the 'more careful' it is, and I believe here the change may be between pronouncing ę very clearly in the slow version and pronoucing it like e in the normal version.
You may also notice that in the slow pronunciation, the one-consonant prepositions are read as if the TTS was reading the alphabet.
Well, if it's talking with someone (having a conversation), that's "rozmawiać".
It's most naturally translated to "talk" anyway, but yes, it can be "converse".
How do the compound sentences like this work? Like what makes you know that the "," is connecting ideas and not separating sentences.
There are rules for using comma before given words, when these words are connecting clauses. The case when "to" connect two clauses of which the second is the result of the first is described in the rule 90.D.1., let. b). Please note, that this is about clauses, and the usage of comma depends on words that it precedes in that function.
All about comma is in the chapter 90 of Polish Writing Rules.