I think Shanks will probably meet Luffy. Some people think Shanks will die before they meet, but I'm pretty sure their crews will meet, since Yassopp is there too and it's hard to see Shanks dying but his crew surviving, unless it's a war, in which case the SHs are likely to be involved at this point. Then again, Shanks did seem to go to WB's ship alone, so there is a chance he could get caught by BB's crew or something while he's going to see someone. I don't think Shanks will become a rival for Luffy. I do wonder why Shanks hasn't tried got the One Piece and if he knows what it is. I wonder if characters who know how to get the One Piece are waiting for someone appropriate to come to get it, because letting it go in the wrong hands could be a problem or maybe getting it will start some kind of war, which they aren't ready for until someone with certain qualities comes along. Maybe it's some government secrets and some of the powerful old-time pirates all already know what it is and Roger's call for the world to find One Piece was just a way to get as much attention on the exposed secret as possible (if Luffy reveals it now, there are way more people who will be paying attention than before the Golden Age of Pirates started). I wonder how much Buggy knows. I don't know if he ever talked about it much.
Idk about Mihawk fighting Zoro any more. Instead, I could see Mihawk losing to Shiryu (Blackbeard crew swordsman) or someone else and Zoro then defeating that person, making him known as the "strongest". As for his motives, I think he wants to see if Zoro can surpass him one day, ever since they met near the Baratie Restaurant.