He cant ignore Luffy's friends.
Shanks dont look down on his opponents. We have seen his reaction to Kid Pirates.
Zoro will be respected for following Luffy. It ultimately makes him a great fighter and Shanks may acknowledge his skills and strength. I think he is not a threat for Shanks yet (EoS is a different story).
Why would he invite him to his crew?
No, he wont ask for a duel. From what we have seen, he likes to avoid unnecessary fights.
He may notice that Zoro is using Oden's sword. But, he may also praise Zoro for being able to use it.
How will he know about Zoro's parents? Roronoa Zoro. There is no specific family or clan name in Zoro's name (i.e., Shimotsuki, Kozuki etc).
I think Mihawk will end up with Shanks in final war. That's how Zoro will meet them.
Zoro wont fight against Shanks, but Mihawk.
Shanks may comment on their fight, but wont actively engage with Zoro (unless Zoro get lost and somehow appear in front of Shanks and challenge him ๐).