Yes, it is a synonym. But it is not really common so I think that would sound a little bit strange. But you can use it as adj without any doubts. For instance: "My dad is respected" = "Mój tata jest szanowany" or "Mój tata jest poważany". :)
It's Accusative actually (looking the same as Genitive). Needs to be added in the hover tips.
The audio doesn't sound good to me. I knew it was "wujek" but I didn't know the case and tried to write it as I heard it, getting it wrong.
"moje" makes no sense here. It's neuter or 'not masculine-personal plural', and "wujek" is obviously masculine.
"szanować" needs Accusative, the masculine Accusative animate form is "mojego". Masculine Accusative is the only situation when it matters whether the noun is animate or inanimate.
I cannot see the relevance of this word at this stage. Since remembering structure is important, why use a verb and sentence example that one is unlikely to use or run through one's mind between lessons?