Rank and Item Luck

Is there a cap on either of these parameters?

Also, I'm rank 10 with level 3 Item Luck. What are my chances are getting a premium item from the Happy Spinner?

I'm level 4 and I have a premium item already

From what I can tell, Item Luck seems to go up a level for everyone 5 ranks you gain. At 20, I gained Level 5, and at 25, I just got Level 6. Keeping in mind that there are 50 ranks, it makes sense to gain 10 levels of it, ending up with 11 since you start with 1. Woo, math.

You can get a rare, premium item at any level, from what I can tell, but your chances are greatly increased when you become a higher level. Or if you buy Happy Tickets, you can just get good stuff, if that's something you're willing to do. Your chances are never going to be overly high, however, to encourage the Happy Ticket buying, because buying Happy Cards guarantees premium items.