Well you're not really supposed to - what you need is a moss stick, a tall one, then you can push the tips of the aerial roots into that.

You can, if they get too all-over-the-place. I've had them eating the carpet behind the sofa. (I'm not a very good housekeeper..) Those ones got the chop - they'd left the mossy stick and made a takeover bid. Today the carpet, tomorrow the dog!

Yipe!!

I've never noticed any problems with cutting them off, but they do regrow. It takes several years, but eventually the base of the plant can die of "old age", and having some working aerial roots can make restarting the top easier.