I'm a firefighter and have helped administer dozens of CPATs. If you are just starting your training, focus on the CPAT. The stair climb is a bitch and I've seen many big guys fail here. The dummy drag also trips a lot of guys up, especially if your legs are fried from the stairs.
If you're in the academy, the PT you're doing should be preparing you for these events, but you'll still need to train events outside of PT. Drag a sled, beat on a tire with a sledgehammer, climb stairs with weights, and run. Then run some more.
If you've been training for 7 years, then you should have the strength base to do most things in the field. But you need to have a big gas tank and use your air efficiently. Most SCBA bottles will only last for 30-45 minutes, and if you're sucking wind the entire time you're working, you're reducing the amount of time you can work.
Start dragging things, doing weighted carries, and running. Then run some more. Again.