He sounds like a creep to me. He invaded your personal space, he was far too familiar, he was pushy, he wanted your address, he followed you home, he tried to invite a stranger from the store to come visit him. That's not normal in any way.
The fact that he's drunk doesn't help.
Him talking about female friends he visits is also icky.
He may not be a threat but I would sure keep an eye on someone like that and avoid them.
It could be wise to write a journal keeping track of any contact you have with him. If anything happens you have a log to show his behavior.
If you know anyone well enough to ask about him you could do that.
I would find it very icky.