Q:Would you mind if I bring someone with me? This is a fine sentence.
A:I would (or wouldn't) mind if you bring (brought??) someone with you. This is grammatically correct but not how we would phrase it. This is more complex because the structure would probably change depending if the answer is yes or no.
I wouldn't mind if you brought someone with you.-- Conditional II requires the past form in the 'if' clause. 'I would mind' is a little-used form except when used in retort.
How about these? Are these conditional sentences?-- Yes
1.Would you be angry if I did this? 2.I would be angry if you did this.