Are they connected? I would like to play the 3DS ports of the Dragon Quest games. (I believe it's 7 and 8)
Are they connected? Can I play them without playing other series?  

1, 2, and 3 are connected as are 4, 5, and 6. You can really play any of them on their own though. Dragon Quest is my favorite video game series, and I'm super hyped for the remakes and upcoming DQ11 this year. I'm sure you've played 9, but if you haven't it's a good way to get into DQ games. I myself am replaying 3 at the moment and then 5, my favorites.  

Nope. I have never played any DQ games.
Also, why 9?  

9 is the newest one in the series(Besides the Japan only mmo), and it was made with newer players to the series in mind, much like Fire Emblem Awakening was. It's for NDS, so go ahead and pick up a copy, or at least look into it.

If you like FF, chances are you'll like DQ as well. It's made by the same company, Square Enix, And it was Enix's rpg competing with Square's Final Fantasy before the companies merged  

Does DQ have a job system like the Bravely series or an epic story like Final Fantasy 6?  

No, to both of those.