Drain cuts. It depends on the type of tile, but typically I will dry lay the mosaic over the drain, take an old drain top, same size and match it up, scribe a line giving a 1/8" allowance around it, take it outside and use a continuous rim 4" diamond side grinder blade on it. First pass just following the line around, progressively deeper with each pass. Too aggressive and it will crack from the heat or shale off the glaze. Takes a bit of practice, use a board or large tile under the sheet for support. I do this all the time and it makes a very smooth, even, round cut.
The uneven slab, I would normally use latex thinset and a straightedge (the longer the better, 10' straightedge would be my bet). Trying to feather with mud you get into bonding/curing/strength issues. Allow it to dry overnight, scrape it over with a margin trowel the next morning to smooth any ridges and shave it as needed. Takes a good eye and a steady hand, as thinset is too sticky to float easily. Once it is smoothed off and before it cheeses up, I throw a little water on it and flat trowel it. Once cured it is extremely hard and performs well.
Oh, and if you use mud to flatten it, wet the slab first and dust it with pure cement for a bond coat. It doesn't have to be 1 1/4" thick (like over wood/wire lathe), because the slab below provides the strength. But it would be tough to make it less than 1/2" bed and, unless you are well-versed in mud, a challenge. I would go the thinset route.