Should a rough wall be smoothed with mortar before installing tile

Here are some good points against using plywood, the source is talking about tiling a floor but most of the points are valid for walls as well.

In my opinion it's better to go the "overkill" route, then have to redo the job in the future because something didn't turn out right.

The cost difference between plywood and cement board is negligible, so your not going to save any money using plywood (unless you already have it).

Do the job right and use cement board, when you don't have any problems and you can enjoy the tile for years to come you will never regret the decision.

When applying thinset, put it on in a flat coat first,, and lay it on thick, pressing it against the wall or floor. THEN go back at an angle and notch it, removing excess. This makes sure the thinset has good contact with the wall over the whole area and will bond well. Laying it on at an angle, so it's notched in one pass, doesn't spread the thinset over the wall nor press it into the wall as well as laying it flat first.

Use a V-notch trowel, definitely; A narrow U-notch will work in a pinch, and don't bother with square-notch; those are for laying floor tile mostly, where you need a lot of vertical play to create a level surface. If the mesh tile doesn't seem to be adhering well to the wall, you can try "back-buttering" the mesh with some more thinset, kind of like applying glue to both sides of a wood joint. Just don't damage the mesh or lose too many attached tiles. Don't be afraid to really lean in with pressure to get the tiles into that thinset; just don't pound on the tiles/wall too hard.