-He looks into my eyes alot with a soft smile and holds eye contact almost the entire time while we're talking
That's just being polite.
-He remembers details from conversations that we had weeks ago.
No biggie there either. I remember details from conversations with MANY people. Even those that I would NEVER have a romantic interest in.
However the other stuff implies that he's really flirting heavily with you. Looks like he probably wouldn't mind being something more. If you are interested in him, just flirt back. The heavier the flirting, the less able you are to "skirt the issue" and he'll eventually almost be FORCED to ask you out. And if not, then ask him out. It is the 21st century!
Alexi