The drain unscrews from the assembly below the tub. Normally the drain and overflow are all one assembly. If you have access to the back/underside of the tub it's a lot easier, because you can control both the drain basket from the top and the nut that captures the threads on the basket from below. However, you can try to replace the basket just using access from above. Easiest way is with a tool called a "basket wrench": An inexpensive basket wrench costs maybe $5 to $10 at a hardware store. You can see how this would lock on to the cross pieces in the basket and allow you to rotate the basket counterclockwise to unthread it. Or you can use the standard DIY method which is to insert two sturdy screwdrivers into the basket, one at the 9 o'clock position and one in the 3 o'clock position, and cross the screwdrivers and use that leverage to rotate the basket. Once the basket is removed, clean the tub surface and install a new basket using a bead of plumbers putty. I will say that the proper way, and the best way, is to have access from below. It's best to set the basket into the putty and then secure it by rotating the nut from below instead of rotating the basket from above.

Yes, the plumbing needs to be done first. Yes, you may be able to just get another acrylic shower wall to cover over everything, if the wall is not moldy or wet behind the tile that you are looking at. There is no need to replace the tub itself if it is in good shape, even if you do decide to take down the wall tile and replace everything from the studs out. Just make sure the workers cover the tub well to protect it while the work is being done. I am with Monicakm_gw, get some more bids for the work. You might want to have them bid on just replacing the walls with new fiberglass, and on doing the whole new tile job, too. You can see new walls at Lowes, Home Depot, and Menard's online. There is also the whole Marbleite wall option to look into. Local dealers for Marbelite are supposed to be cheaper than buying from big box stores, if I remember right. While you are fixing plumbing, you should probably put in a proper mixing valve to protect from scalds. It is the code now. No one will be able to turn the water too hot to burn themselves and flushing the toilet or using the water elsewhere in the house will not burn the person in the shower anymore, either. I have read the experts here on the forum say that the Symmons Temptrol system is very good and is a good value. Here is one that comes with the shower head and tub spout for under $100. http://www.homedepot.com/p/Symmons-Temptrol-1-Handle-Tub-and-Shower-Faucet-in-Chrome-S-96-2/100643619

Thanks. My fabricator has screwed up many times on my quartzite. The island is on crooked. He had to redo the perimeter countertop because he only measured for length. He also had seams that were 1/2" wide when I had told him no seams at all, and 1/4"-3/4" gaps along the back wall. I had two matched slabs set aside, so instead of using the 2nd slab to recut the perimeter counter, he found a cheaper slab that was a different color and had a different texture. He sees nothing wrong with the slab being different. When I asked him last week about fixing the hole where they cut the drywall, he said, "We always adjust the fit that way." He has been in business a long time. He is not going to fix the hole. I never have water there, but my husband has his coffee pot there, so a spill is possible. I just need to figure out how to fix the hole on the inside of the bathroom wall before we install drywall. I know I can caulk it on the kitchen side. Pet screens...I have never heard of that. We live lakefront, so we get tiny bugs that can get through the fiberglass screens. If they are non-metal, do you know what they are made of, or which brand of windows/screens you have? Maybe I can find them. I don't know of any surplus stores, but maybe some have opened in the last few years. We have spent a lot of money on things you can't see in this remodel...beams, complete rewiring of electrical and plumbing, 2 heat/ac units, new stairs, roofs, gutted the great room and kitchen, etc. We also had new siding installed on the house, and turned a huge upstairs room into 2 bedrooms, a bunk room, and a sitting room. Now, we are about out of money, and we have 3.5 baths to remodel, new carpet for bedrooms, and need to refinish a 1400 sf hardwood oak floor. I am good at budgeting, but the $35,000.00 ceiling beam was just one repair that took a chunk out of our budget. Rather important beam so the roof wouldn't collapse!

Beth - Wow! Thank you for all of these suggestions. I painted my vanity black and it looks beautiful and I am getting polished brass/gold handles and fixtures. I have not yet bought the top but, because I could only find one quartz option in a white that looked good with the bright white tile and the carrara marble of the greek key trim and the porcleain floor tile (looks exactly like real carrara), I decided to look for quartz that looks like black marble with the white veins (will then match the black marble of the mosaic and the black marble look porcelain that will be cut into 3/4" strips to make a liner around the entire room on the floor) after finding out I would need to buy a huge slab (enough for 3 countertops). I am finding the same issue with the having to buy full slabs for the black, too, but at least there are more options that can work. I found one at Home Depot that would be great but can't wait for their installation and they won't sell unless they install. So now I am looking at this https://www.elitestonegroup.com/grey-sparkle-1733.html since the sell in small sizes. The only concern I have is this brand has only a 1 year warranty compared to lifetime with all these other known brands. Anyway, I was thinking that a black on black vanity could work since there will be so much white on the walls, the ceiling will be white and the floor will be white. And thinking the gold fixtures will look more striking against the black. The faucet that I got is actually featured on a black on black. I was hoping to get a more subtle white veining like in this picture (the Home depot Viatera has that - https://www.homedepot.com/p/VIATERA-3-in-x-3-in-Quartz-Countertop-Sample-in-Capricorn-LG-H023-VT/311102604 - I wonder do you think I should risk waiting for Home Depot installers for up to 6 weeks to get this one or do you think ok to get one that has more prominent white veins since I have a lot of white on the walls. I am also torn on if I should get the sink in black or white.