"dad" is "tata" (although in this sentence you'd want vocative "tato")

I translated it as well!

Same

'Goodbye' would be 'do widzenia' in Polish.

same :(

Yes. "DZ" is from "gods", or "woods", DŻ is from "jam" or "jungle".

However, this is the third one from the family. When you have DZI, that equals DŹ (it's not that visible in Duolingo font, but that's what people usually call 'accent', and not a dot like in DŻ). And DŹ = DZI is palatalized DZ. Palatalized sounds are difficult for most of foreign learners. It could help to listen to the comparison in section two of this website.

Other pairs of palatalized sounds are Ń = NI, Ć = CI, Ś = SI, Ź = ZI. It's a matter of orthography mostly, although sometimes there will be a hearable difference between just having "ń" and having "ni" which will make a separate "i" sound after the palatalized "n".

the "e" with accent is spoken as a nasal. That's why it sounds a little like a "n"