Can I repair carpet? Vinyl? Ceramic?

Probably! Should you drop something, stain or damage your flooring, a trained installer should be able to fix it and get acceptable results, as long as you saved extra pieces of the original material. Your warranty through Lowe's does not cover damages to flooring, so, there will be additional costs to you. Please contact the store you where purchased the carpet and explain to the flooring specialist what happened so they can get the ball rolling on the repair.