Will 82-081 work for a Milgard door

The 82-081 isn't exactly like your old handle set but it should work as a replacement, yes. It comes with a key. There's no need to buy one separately. There shouldn't be anything else necessary to make your door lockable from the outside, all you need is a key cylinder.

No. Like I said, the 82-081 already comes with a key cylinder. When I said "that's all you need," I was specifically addressing your question "Is there anything else needed to convert the current door to be lockable." The answer to that is also no. All you need to make a door handle set like this lockable from the outside is a key cylinder, which is fortuitously included with the 82-081 set.