What Are My Rights As Tenant Of Apt In Disrepair Since Mid-nov?

Location: Detroit. Apt partially uninhabitable since mid-Nov from a burst pipe(supposedly). It's now end of Jan. Lease is up end of Feb. I've been paying rent anyway bc I heard escrow at your own bank isn't useful legally, although now I hear otherwise. I'm worried the room is not entirely dry and there will be mold even after repairs. This is my daughter's room, I dont want to play around w her health. Can the city buildings dept inspect for insufficient repairs after it's done?

I wanted to be moved to another unit same sq ft & flr plan at my current rent, which is $500/mo below market. No rent caps in Michigan, but I have a track record of little to no rent increase signing anew for the last 7yrs. They offered a transfer to another unit at market. Imo, the transfer request is a lateral remedy in response to the (non) repairs, and should not be confused with a renewal negotiation.

I should have put my rent in escrow huh? Should I for Feb? Is this going to shoot me in the foot for renewal negotiations? Lease reverts to month-to-month after current contract ends. They will try to force me into market rate if my lease converts. Either way, increasing rent by about 50% either bc of month-to-month conversion or transfer to comparable unit, would be considered retaliatory bc of proximity to repair complaints wouldnt it? If I ask for abatement, am I going to open myself up to facing market rate increase next year when I have to renew again? How would I bring this issue to court?