What the title says.
I hope I got the right forum for PF 1 adventures.
Hell's Rebels has quite a bit of roleplay. Curse of the Crimson Throne does as well.
No AP starts at 6th. They all start at 1st. That said, it wouldn't be terribly hard to level things up a bit and slow down PC's XP progression.
There's an Adventure Finder by level for P1e on the site. Here are the ones that start at 6th level. Looks like The House on Hook Street has great reviews, but I don't have any experience with it myself.