4x4 shower drain is more than enough for a 5x3' shower base. Keep in mind that the drainpipe is not changing only the square portion does so the water will be draining at the same rate.

It depends on the size of the tile. If you're using 3x3 tile, then use the 6x6 drain cover so that the tile can line up perfectly with the drain. If you're using 1x1 or 2x2 tile, then either would work. Of course, this only matters if you have a good tile setter that pays attention to such details. Hopefully you have one that does.