We had painting done and some paint got on blue slate in our entranceway. It was cleaned before drying with water but a modest milky film remains. I've read about alcohol or mild dish detergent (Dawn) but have not tried anything. I also considered 1,000 grit sanding. I don't believe the slate is sealed. Thoughts please on the way to remove it.

I'll preempt this by saying I'm a tile amateur. Prior to this project, the only tile work I've done is a small 7'x5' patio. I'm in the middle of a bathroom remodel and have run into a pretty big issue. The back story - I put in a built in niche in the shower, and wanted it to line up perfectly with the grout lines. I set the pan, water proofed everything, measured and remeasured and put in my niche. After reading a couple of other forum posts, I started my first course of tiles at the bottom of the niche (using a ledger board), to guarantee no cuts. I then proceeded to tile the whole shower from the ledger board height on up. The plan was to then come back, lay the floor, then put in the two remaining courses. Well, you guessed it, I miss-measured. When I place two tiles up to the wall, I end up with 3/4" - 1"" gap. So - any creative ideas as to how to overcome my issue? The only solution I've come up with is to use two runs of Schluter Quadec stacked on each other to take up the gap. One other side question - the flooring in the shower is stone mosaic, and the walls are porcelain with glass tile mosaic accent. The floor calls for sanded grout, and the glass tile calls for nonsanded grout. I'm concerned with matching color and texture. Any thoughts on this as well?