I have a few questions:

1) "мы не могли радоваться лету и отдыху."

I believe лету and отдыху are in the dative case. Is this correct and why would this be?

2) Also, in this sentence

кот залез под дом

why wouldn't дом be in the instrumental case?


3) выхода оттуда не было

Why is быть сonjugated for a neuter noun? Shouldn't it just be был since выход is masculine?