Well, the screen tearing bug still exists in GMStudio, to a point. It only happens on certain cards and drivers. A guy who works for Yoyo confirmed with someone from either NVidia or ATI about it, that it actually has to do with some kind of GPU difference, making things a single pixel off at times. It is actually easy to get around I'm understanding if you draw the whole thing to a surface(render texture in GM) and draw that full screen, which even allows for post-processing effects easily.

About actual game engines, etc... I'd say overall the most popular appears to be Unity, especially for 3d. I'd say the reasons are basically what all it can do for a very cheap price. The free version has some features that aren't in the pro version, but they aren't that big of a deal. Also, for you, I don't think it would be an issue to use C# with it. There are differences from C++, but not that much.

If you want something a little lower level, Ogre3d is a good contender. I don't use it myself because I stick to GameMaker and Unity, but I've messed with it in the past. It is somewhat bloated, and not quite as fast as it could be, but it is really pretty good overall, and is used a lot in the indie community, though not as much as Unity at least I would think. Also, it is basically just graphics, so for sound, physics, etc... you will need to roll your own or bolt something else on.

FWIW, with C++, I use SFML for all my rendering, input, sound, windowing, and system needs. I also typically use a 2d physics library for movement (I make only 2d games) such as chipmunk-physics or box2d. For making levels, I've used both tiled (tile-based) and gleed2d (free-form). And, I use raknet for my networking needs. (You can google all those resources)

Good luck!