If I have a key that opens one door, can I take that to a locksmith and get a master key to all similar locks?

Nope. It doesn't work that way. Although, you can ask your locksmith for a bump key or a 999 key. It's basically a blank key for the locks that you have filed down to maximum depths. However, most locksmiths are not comfortable giving out bump keys. This is why most people just choose to make their own bump keys.