You have to be at level 15.
As you level up, you will be able to level up your dragons more. You simply need to grow treats and feed them.
Well to make a swamp dragon you need water and earth. You get water at level 14 and you also can buy it at level 14. So it's level 14.
First you have to buy the Perch of Kairos. Then, you have to collect all of the pieces you need. You can get them by sending your dragons on quests and racing in the Dragon Track. Once you get all the pieces, you'll get Kairos!
You will need to just work on leveling up. It shouldn't take long. The first gemstone dragons come available at level 12.
Yes, you must have an active internet connection on your iDevice to play DragonVale.
To get the racing car, you need to complete level 4 of the car salesman adventures. After you do so, the Hellenbach GT is available.
You can't play it online. You need a iDevice to play it.
You can't breed these, you need to buy them with your coins.
building level 2
To answer your question, you will need to buy a Colosseum which costs about 50,000 coins in dragonvale. Other than that I don't think there are any other contests to come yet.