I rented out my primary residence for a while and has a passive loss carryover. I heard that I cannot use it until I sell the house.

1) Can I offset it with other passive income such as investment income?

2) When I sell the house, how does the passive loss carryover affect the primary residence exemption? (let's say my gain was $300K and the exemption is $250K (single) so I have a taxable gain of $50K and the passive loss carryover is $10K)

In theory, your capital gain would be reduced by $10K. You CANNOT claim the loss against investment income.