I have square casing around the top inside my entire house. Also, I have one of those tile ceilings, where the tiles rest on each other. It looks like crap but it is low on my list of things to replace right now. Can I replace that moulding without any fear of these tiles falling out?
You should be able to, those type of tiles are usually stapled on.
If any at the perimeter want to come loose, us a brad nailer or
air stapler to tack them back in. If no air tools, 4d brad nails
at an angle will also work