home improvement centers have floor scrapers they will rent to you. they are a heavy machine with two wheels and a vibrating blade in front that you walk behind, great for pulling up tile, carpet, linoleum, etc. . .
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yes you can, but that doesn't mean that it's the best solution. the best way is to remove the old tile. period.
You risk having the loose tile cause the grout to chip out. Find a way to secure the tile first.
Make sure the sub surface is clean.If it is not cement,you would have to add additive to the thin set addhesive to bond to the floor.Lay out floor from center of room off both walls.Snap line on floor to form a grid to fallow.Place the tile's in the grid depending on the size of the tile.If you lay 4 tile's on floor as example leave space for grout.You will have your grid square.With a 1/4" notch trowel place mixed thinset in the grid.Then apply some thin set to the underside of tile with trowel and remove excess with trowel for a good bond.If you place thinset on floor only and don't apply to underside of tile,they will all come loose in a matter of time.Good luck
You would be better of removing the plywood floor completely - and tiling over the original surface.
The best way to figure out how many 13x13 tile will be needed to cover 30 sf of floor is to calculate 13x13/144 give coverage per tile (1.1736), then take 30/1.736 = 25.56 tiles.