I am planning to install ceramic tile 50x200mm to brick wall as a splashback in kitchen. There is less gap with sink tap and brickwall so there is no enough space to add plasterboard on brickwall. Before there was old tile on splashback which I have already removed and there are small chipped on brick and not so smooth surface and gap between brick because of mortar. So is it ok to install tile directly to brick wall. If so what could be the best tile adhesive I can use and what thickness of trowel is good to use.
You should use thin set. Preferably a modified thinset, unless the tile manufacturer recommends against it.
The size of the trowel will also depend on what tile you are using. It is difficult to determine an exact size without knowing more about the tile you plan to use. Generally you will want a thickness of mortar that will fill the gaps and voids and still leave ridges above the surface to contact tile.
More info about the tile and maybe a pic of the wall and we can get you a more detailed answer.
Use thin-layer mortar to make wall flat, remember to wait as long needed - check mortar description, then use choosen water resist layer on wall and if possible on floor, then put tiles on chosen adhesive (mortar or glue) Read instructions on boxes/bags and do what is writen - if need some additional steps then it shall be writen in product description.
Or hire proffesional.