Adventurers are the rock stars of my world.
Is adventuring a fairly common profession?
1st level adventurers are like a group of kids getting together to form a band - it's not something the majority do, but you probably know
someone who's had a go at it. The ones who make it out of the first tier are equivalent to the ones who do well enough to get an actual contract. And those who make it to the highest levels are equivalent to Queen, the Beatles, or the Rolling Stones - virtually nobody makes it that far, and virtually everyone has heard of them.
Of course, all of this is pre-"American Idol"/"The X-Factor".
Are there adventurer's guilds and taverns, bulletin boards posted with adventuring jobs, laws and conventions governing adventurers' conduct?
Not as such. But there is a network of people out there who want things done. So low-level adventurers probably can find adventure if they ask the right person. Or they can just head out into the wild.
Once they get past the low levels, the PCs will find themselves much more in demand, with people coming to them with work. They won't need to be so self-motivated... but they will then need to be a bit more choosy in what they do.
(Also, there aren't any laws or conventions as such, but if you get a reputation for being 'difficult', don't be surprised when people stop booking your band!)
Is their lifestyle precedented at most by heroic myths and legends? Does the rest of society not quite know what to do with these heavily armed wanderers?
It's not unheard of for adventurers to hire bards to go around spreading their legend far and wide, or otherwise self-publicising (see: Gilderoy Lockhart). Of course, that can all go wrong: when danger reared its ugly head and they bravely turned their tails and fled...
And, yeah, society may well have difficulties dealing with the arrival of a band of adventurers - in exactly the same way as if a big-name rock star rolls into town. Which may be great and all... but what happens if said rock star starts making demands, or his entourage start abusing people, or...