I already have a level 2 dragon on my army camp and I'm waiting an hour to be upgraded in the laboratory to level 3. Would the existing dragons on my army camp be upgraded also to level 3 or would they still be level 2?
All units you currently have in your service will upgrade to the new level. As you have dragons you can easily see that because they will change it's color. You can also save some elixir by filling your queue with the "old" dragons and getting the new one out when you again have space.
Source: Personal experience
Yep, they will also upgrade to level 3.