Check in luggage?

TSA has the right to visually inspect checked bags. They don't open every bag, but they will break into a bag that is locked with a non TSA compliant lock if it is selected. Get a TSA compliant lock; they can open those without damaging the lock if they need to inspect the bag

If you don't use a TSA approved lock and you lock it, I can practically guarantee your luggage will be chosen for inspection.

You can lock it if you use a TSA approved lock. They must be able to access your bag, if needed, and will cut off other locks to do so.

They don't open every bag. They open bags in which they see something suspicious during scanning, and sometimes they do random hand searches of bags.

You MUST use a TSA approved lock otherwise they will cut it off and throw it away. You can use a TSA lock (although I have had a few of those thrown away too).

Yes lock it, always.