I don't think a membrane is enough over a vinyl. A membrane is only used over a properly installed substrate and old vinyl flooring is definitely not a proper substrate. 1/4" durock or hardi board are what you should use. Thinset will not bond well to the vinyl and will start cracking as the vinyl expands/contracts with temperature. I've been doing tile a long time I would never go over vinyl with it. Way back in the day before concrete board and membranes, we still wouldn't put tile over vinyl. We would have used a layer of 1/4" luan. Screwing down another layer also insures the subfloor is solid.

You also need to make sure the floor is perfectly flat when using the tile you are using. Due to the length of them, any high spots will cause major headaches at the joints. The bigger the tile, the more perfect the floor needs to be. You can use a large notch trowel for a thicker mortar bed to compensate some.

As for dry laying, it rarely works out and there is really no need for it. You don't start at an edge. You start in the middle. Find the center of the room and break the room into 4 equal squares. Start at the center and work your way to the wall. in a stair step pattern to keep the tiles running square. Figure out how many tiles( the 6" side) it takes to go from the center to the wall. If the cut at the wall is less than half a tile, shift your starting point a half tile over the center line. This will make your cuts at the wall all be over half tiles instead of little slivers.