Novice floor tiling question(s)

I have a small (appx 1m sq) area of floor where a built -in cupboard was removed. The inside of the cupboard was not tiled and I want to tile it to match the existing floor (I have spare tiles). The existing tiles are laid on a cement bed re-inforced with wire mesh over a polythene membrane.
My first question is; what mix should I use to bed the new tiles on does it need some sort of adhesive additive?
Secondly, some of the existing tiles are loose and as it seems impossible to cut out the cement bed without then loosening the buggers in the row behind! is there something I can use to stick them down without raising them up too much above their neighbours?
Appreciation in advance Adam

Use a 5:1 sharp renderers sand, cement mix, or just a bag of pre-mixed mortar. Mix it fairly dry, and screed it level about 5mm below the bottom of the existing tiles. Wait for it to dry, and use a 10mm notched trowel to apply tile adhesive before bedding the tiles in. You can stick the tiles directly to the wet cement bed, but it requires some expertise, or your tiles will be drummy.

Just use max bond, or silicone to glue down any loose tiles. spread a thin layer over the back of the tile, as well as on the bed.

:2tsup: Many thanks John, the existing ones have been laid direct onto the cement bed and they pop off for fun so I think I'll take the option to screed and then use adhesive.
Thanks for the advice. Adam