Is "Nos" in "Nos domi studemus" optional?
Yes. There would be more emphasis on 'we' if the nos is included.
Thanks for clarifying.
Which case is domi? Because I thought domum is accusative and domo dative. But this is different again
domi here is the locative case (which only occurs for names of cities, towns, small islands, and a handful of other nouns including domus).
So when do we use domo?
For movement away from home.
domo venio -> "I am coming from home"