Is it really not the done thing...

My wife and I were really close really quick. We actually slept together the first night we met and we've been together ever since. Just don't expect the other person to move as quickly as you want them to and don't force things.

??? isn't that stuff people do before getting married? I don't think it begins after marriage....I think it's that comfort level that tells them it's ok to marry each other

Those things sound perfectly acceptable for a first date. In fact, those things might be a nice way to help ease a friendship into something more.