Can you install new ceramic tile over old ceramic tile? (small room)

Yes! Here's how: https://www.familyhandyman.com/tiling/tile-installation/tile-installation-how-to-tile-over-existing-tile/view-all/

Not recommended. It raises the floor up too much and the mastic may not adhere correctly to the old tiles. The old ceramic may come up easier than you think...

Yes you can. But it is easier to install them after the old tiles have been removed. You have to watch your edges as installing over old tile will significantly change the height of you tiles. You must make sure the new height won't interfere with doors or openings,etc.

Why are you wanting to put new tile over the old stuff.... is it just ugly? or is the old tile broken or loose..? If the old tile is broken or loose... you really need to remove the old stuff... otherwise it will be like installing tile over a carpet... just... wrong.. and the new tile will be just as loose as the old stuff.

I have heard of installing laminate or engineered wood flooring over tile... but not tile over tile.

You need to remove the old ceramic tile before installing new ceramic tile. Laying tile over tile will cause big problems.