There are quite a lot options for this, each with different features, strengths and weaknesses. A few examples:
Gazebo (as mentioned by edwinem): very well known in the robotics community, some would say it's a little bit dated
Microsoft Airsim (also mentioned by edwinem): originally developed for autonomous drones and autonomous driving, uses the unreal ...
I have never used it ,because I have always dealt with custom simulators but I know others have had success with the RotorS simulator.
Answers to your questions:
1) Can I modify these models so that it can simulate my drone? Is it enough to change the geometry, mass and inertias to make it work?
Kind of. You could just take one of their existing models,...
If you want to test everything together then you need to setup a simulator like Gazebo(integrates well with ROS which I assume you are using). Other options could be Airsim, or some custom simulator. These options though and are more involved in required setup on your part.
SLAM is pretty easy to test. Just download some dataset such as ...