On our Lease Agreements we charge a $250 non-refundable cleaning fee also.The landlord can do what he wants with it, as it has nothing to do with how the rental is returned. The renter is responsible to return the property back the same way they got it, minus reasonable wear and tear. All the light bulbs need to be working as they did when they moved in and the carpet needs to be clean as it was when they moved in.(if you lease says that)
If the door handle was documented for a repair, but broke again, you should have reported that so they can get the repair person back to do the job right. Seems like they need to be reminded about the previous repair.
The legal daily rate to charge has to be prorated so if you rent was $900 it sounds legal.
The resealing of the faucet seems odd. I wonder what would have happened if you called the landlord during the lease to report that issue? Would he have fixed it then without charge? it is hard to say without all the details. I always tell my renters to call in issues as soon as they become a problem because they will normally be cheaper to fix sooner than later. Hope this helps a bit.