Can a shower and tub share the same drain?
Of course they can as long as you have proper drainage angle and double venting and traps. If this is an installation of a new fixture, you need a permit and a master plumber to sign for the permit. Get a plumber and do it right. Just asking the question tells me you don't know what to do and could get into trouble. Saving a few bucks and doing it wrong will cost you so much more in the short and long run. Some things have to be left to the licensed professionals.
Yes, they will both be using the same drain pipe at somepoint inside or outside of your house.
But the the pipes must join well below the level of both items or the pipe must be large enough for the combined flow, otherwise when you put water down one of them, it will flow out of the other!
yes sir. most modern home are build to allow both to share the same drain.