Can you use a canon ef 80-200mm lens from an eos 3000 slr camera on a canon eos 400d?

Probably. Check the compatibility chart near the back of your owner's manual. You might lose some of the automatic features, but I am not a Canon expert............

There have been compatibility issues between digital cameras and non digital lenses.
Look at the make of the lens and contact the manufacturer to ask if it is compatible, many are not and you will get E900 errors .
This happened to me a few times before i found out that they would not work, not all lenses will act this way so you may be lucky.

It is an EF lens. It should work.

Just call canon and ask.

If it is a Canon lens yes you will be OK. Other vendors (Sigma/ Tamron/etc.) may not work.