Depending upon the type of system you have, it is usually possible to install ceramic over radiant heat floors. Some applications will require a membrane in between the tile and subfloor. Ask your contractor what is best for you.

Yes, vinyl is very appropriate for basement use, but like all other flooring types, check to make sure you do not have a moisture problem before installing it.

Vinyl is certainly not as resistant to tears and scratches as ceramic tile is, but most vinyl does have an inner layer built into it now which tends to resist tears quite well. I wouldn’t hesitate to consider it in a high traffic residential area.