Recent air travelers: some baggage guidance please?

I haven’t traveled by air in 9 years. Now I have a trip coming up, and my experience is very out of date.

Am I allowed to lock my checked bags any way at all, even with a plastic clasp?

What happens if a bag is overweight?

Are carry-ons a big problem?

Have you been closely searched by TSA?

Any other hints and cautions?

Thank you.

Tags as I wrote them: travel, airplanes, flights, baggage, trips, luggage, TSA, security.