the sheet tile and the tile is smaller than the four by four ones, you might be able to get along with only nippers and the saw blade that you attach to a hax saw.
Jay, mortar and adhesive are two different things. The mortar is actually called floor levelor or skim coated base. The adhesive you are referring to is called mastic, and you do want water proof mastic.
Laying the tile to the wooden floor might not be advisable due to the movement of the wood causing an unstable sub floor for your tile.
If you use the four inch by four inch tile, it has built in spacers so that the grout lines are uniform. In all the places where I have bought tile, you can rent a good quality manual tile cutter for little of nothing.
You really will have a hard time cutting the smaller tile affixed to the sheets.
If it was my tile job, I would use the larger tile. But, this is your call.