The tart pans I have are 2 parts so you just push up from the bottom & the tart comes right out. I never have a problem. However a year or so ago, I made a lemon tart with just a freeform tart ring (sort of flower shaped) with no bottom & put the dough in the ring & prebaked it on a cookie sheet. It was a lemon tart from the Joy of Baking site. The crust was so tender & flaky it shattered when I tried to remove it so now I bake it in the 2 part type tart tin.

Call a tub refinisher.

Shake outside, then wash. Polyester fleece usually softens up quite nicely after machine washing and drying. If you put the dusty things in the dryer, they'll get dust all over the inside of your nice clean dryer.

When it is 'black' like that it indicates the RAW wood has been exposed to the minerals in DIRT or water (I see water stains/intrusion at the base of the wall where she's nailing). The 'dirt' is gone but the MINERALS remained LONG ENOUGH to stain the wood (not the finish...the wood itself) a black colour. This is an indication of wood damage...not finish damage. There is no scrubbing that will remove MINERAL STAINS in wood....you need to sand PAST the black stain (honestly....look stains in hardwood floors...you will come up with THOUSANDS of photos). There is no other way. Notice the black stuff to the right...that's water damage. The water evaporated but the MINERALS in the water remained long enough to stain the wood BELOW the finish. There is no cleaner in the world that will get rid of that other than a floor sander.