I use GameMaker Studio, and own the Master Collection.
For 2d games, I don't think it can be beat at all by much of anything, unless price or graphics features are the only factors. Consider this. Unity has the free version, which I admit is really good, especially for free. For 3d games, it is probably the best in general free thing to use. But for 2d, not so much. Unity's 2d is pretty far behind GMStudio's capabilities, especially considering the recent updates to GMStudio, which include the use of vector graphics, and multi-platform shader capabilities, which let you do many things. GMStudio's 3d isn't very good at all, but at least with the shader system(which also works in 3d) people have created deferred renderers, shader based skeleton animation, normal mapping, among other things.
The biggest barrier to GMStudio is the price, at least for just getting started or if you have zero budget. Unity will be harder to get started with, but you can do so for free. As mentioned above though, who knows what will happen to prices now that Epic has the $19.99 + 5% pricing going on? Unity so far hasn't announced anything, but that doesn't mean nothing will change. GMStudio, though it usually is considered at a lower level(just because it is meant for 2d games), may or may not make a pricing change, simply because it is still overall a good deal.
The biggest "feature" of GMStudio is generally how quick and easy to get things done it is with it, combined with the capability to do pretty much whatever you want via the scripting(GML) and shader implementation, combined with the multi-platform support it provides. The amount of platforms it supports at the moment is massive. It has all of the major ones, and a few minor ones too. In fact, except for consoles, it supports more platforms that Unity does. It supports Tizen and HTML5(including WebGL), neither of which is supported by Unity, though Unity currently has a web browser plugin and they have WebGL in the works if I'm not mistaken. Basically, the point is in this package you get speed and capability in a very good balance.
I guess I can confirm answers to the actual questions too.
2. For graphics, you can import several file formats. The best one to use in my opinion is PNG, due to it having good support for alpha channels. In the newest releases, it also supports flash graphics, though it is likely to have some rough edges as it is not in the stable branch yet.
3. Yes, and you could render said character into animation frames(sprites) and load those in, or you could learn how to use GM's 3d and convert the models into file format that you can either find code to load or code yourself the loading into GM. 3d is a pretty weak part of the software though, so you won't find support for many 3d things internal.
4. Cutscenes...you can roll your own pretty easily using timelines. It would work like any other parts of your game though, either simply showing a few images one after the other(like comic books) or using in game graphics and making them move around via code(instead of player input). If you want actual video from a video file, GMStudio doesn't support it internally.
5. I think you can use the free version to publish to several places, including steam if I'm not mistaken. But, the free version of GMStudio is truly more for evaluating, not like Unity's actually useful free version. GMStudio has limits to resources in the free version and doesn't export to most of the platforms that it supports.
6. It depends on what kind of career you want. Alone, GMStudio wouldn't get you a programming job, as you would have to learn programming languages used on said job. As far as game creation goes, it very well could help move a career along, especially if you were looking on the art side because you can easily get your art into your games. It could also help with contracting work, as in somebody pays you to make a game, due to the above features it is good at that. Lastly, there are more than just a few people who have gone indie using GameMaker, even version before GMStudio. Some of that is a testament to hard work, design, art, etc... and not only the software, though the software does help make things faster, allowing games to be produced in less time.
7. It does support iOS and Android(including OUYA). The prices last I checked were $799 for the Master Collection, which includes everything. The professional package is $99, which includes a few exports, but then you'd need $199 each for Android and iOS, so it could very well be a better deal to get the Master Collection.
8. At the moment, there is no officially announced XBOX ONE support. PS4/PS3/PS Vita exports(which you would get with a Sony Developer's package/SDK) are still in the works, with planned release dates of April 30th/May 30th/June 30th respectively. Note that this assumes you get approved by Sony as a developer, but then you'd get GMStudio with those exports for free if I have it understood correctly. There are rumors flying around that Yoyo is working on support for XBOX ONE and/or WiiU as well, but there haven't been any official announcements made that I have seen yet.