Tiling advice - surface preparation

Hi everybody,

I have never tiled before and require advice wrt surface preparation for a kitchen splashback using ceramic mosaic tiles. So, here is a lot of dumb questions:

The existing substrate is what looks to be plaster, over the top of a dark grey, cement render kind of substance, which is applied over bricks.

There is a small (1m square) area where the old tiles used to be that is grey render only, as the old plaster may have come off when the old tiles were removed.

I know it's not rocket science, but what do I use to re-surface the plaster-like finish? Skim coat?

Also, there is a small area where the render has come away from the bricks. What do I use to fill this area in (it is about 1.5cm deep) - what is this stuff called?

Any advice is appreciated.

FishHead