Yes I can.

Both mean god, God of Abraham and deity.

They're so, so different though. If you take the literal definitions of both words, sure. The connotations of these words are not the same.

Probably. Though it's unlikely that it has anything to do with Dajbog. What about the phrase "ako Bog da"? It follows the same pattern of using "bog" as reference to the God of Abraham.

Serbians now are for the most part Christians, so naturally, any expression would be modified to suit. In general, where the word 'bog' is involved, you can be sure that people used those exact sayings before Christianity. Perhaps 'bogovi' was used instead of 'bog', or perhaps they were referring to a supreme god.

Why would it have anything to do with this particular god? What is the logic?

I explained it ^ above. He is the god who gives.

Who says this? According to most Slavists Perun was at the top of the pantheon, though I'm not sure how we know these things since pre-Christian Slavs did not write down these things so we can only assume.

This varied greatly among different groups of Slavs, it seems. If you search this forum you'll find people talking about it, Cvetinov in particular. I can't remember where I read it, but it has come from numerous sources, that's all I can say at this point.
In any case, I am absent strong feelings on this matter, I'm playing the devil's advocate more than anything.
Done is done, we'll never know.