Have you tried removing any of the tile? Sometimes, if you hit them right with a chisel between subfloor and tile they'll just "pop" off. Left over morter and grout, depending what it's adhered to can be easy or a bitch.

I'd take it off.

What says. Try taking it off first. Installing a floor over tile is just asking for problems later on down the road/

What's beneath the tiles? If concrete, and if the tiles are not coming loose, then using leveling compound over them should be fine imo. Clean off dust and dirt from the tiles before applying it.

If the tile is on solid and it will not create a big height difference you can tile over tile I've done it but the tile I went over was fucking on the underlying concrete God damn rock solid. So listen to these people try a test area if it comes up easy take it all off.. if it doesn't come up easy and is level go over the top and it will be fine the floor I did is rock solid still.

It always good to start with a solid foundation...

Why not plywood or osb? You might get away with filling in the grout lines with more grout but you might not too.

Can you take a pic of the tile?

No

Won't you then have bubbles, lines, or dips where the grout lines are?