Making games is not rocket science. All you need to do is to learn a game engine like Unity or unreal. The second thing is to come up with a game idea for your game. Then uses the Game engine you have learnt to make the idea into a game. Read more

As such there is no requirement for a qualification to start making video games. But, if you are planning to go and work for a game development company then, a basic college degree along with knowledge on one or more game engines will be needed. Also learning a coding language like C++ or C# will help too. Its always better to make a portfolio of games that you created before applying for a job.

Game designer is a creative job and game developer is a technical one. Game designer ideates the game mechanics, art, music etc. Game developers are people who implement the idea and make it into a playable game. In most indie studio, game designer and developer is the same person. AAA studios require someone to maintain coordination between different development departments. So, they hire game designers seperately.

The best thing is to make a small game yourself using a game engine like Unity. Your first game should be as small as possible. Take a look at the Youtube video by extra credits on how your first game should be.
If you are looking for a more step by step process. Here is a link to Unity's tutorial on making roll a ball game, start from here.

It doesn't really matter which game engine you use to make a game. What matter is whether you make a game or not. If you are already proficient with any programming language then choose the game engine that uses it. That way you will be able to learn faster.
if you are planning to get a job in the gaming industry then try to learn Unity or Unreal, as they are the industry standards in game development.

Yes. The revenue of gaming industry is greater than the movie and music industry combined. Where there is money there is opportunity. As per Glassdoor the average salary for a Video Game Developer is $83,739. Which is not bad and it goes up as your experience increases. The only thing that you need to decide is which part of game development(art, programming, sound etc) you want to work on.

Both has its own merit and demerits. Better not to go indie if you don't have anything to support you financially. Not all Indie developers succeed in their first attempt. You should know that angry bird was the fiftieth game for Rovio. Though, the self publishing options have gone up in recent years the chances of success depends on lot more factors than just making a good game. It is better to have a few years of experience in a game studio before going indie.

If you have planned to get into game development before your college then getting a relevant degree will be helpful. But, as such its ok to learn game development online through YouTube or websites like Udemy. All that matters is you are able to come up with a portfolio good enough to convince the employer.