"Is it mine?"
Translation:Er den min?
It is now, although you should probably write "Er det mitt" instead.
They should be of the same gender, like "er den min" or "er det mitt".
'det' can also be used as a formal subject, for instance when introducing new things to a conversation: "det er en stol".
Then why is "er det min" right? The current options do not include the two that you mention.
They should, but as you've noticed, 'er det min' is accepted. But this doesn't really follow any of the rules, and is merely an exception, where 'det' is an unspecified object.