How to transition from lectures/exams to research/thesis?
Firstly, don't worry. This anxiety that you describe is extremely common and completely normal. You're right that it stems from the transition from very tightly-constrained styles of work to something that is much more open-ended. You are half-way there - you have recognised that you have many different possible paths to follow. But I get the impression that you are still thinking in terms of pass and fail. You talk about finding the "right decision", and that a given approach "might fail or not", but research is not so black-and-white. 

Of the many different paths that you are considering, it's not that some of them contain death-traps where you will be forever doomed, whereas some are shining paths to glory. It is likely that you can make a success of any of them (just so long as you don't stay rooted to one spot for too long...). Even a "failure" to find a solution is useful. In the words of Thomas Edison: 


  "I have not failed. I've just found 10,000 ways that won't work."


You might find inspiration for something else, or you might just be able to rule out one method - that is still progress.

You also talk about whether to pursue a single issue in depth, or take a radical change of direction. Both those approaches are valid, and it's up to you which style you prefer. Eventually, with experience, you will start to get a bit of a nose for what sorts of approach work best for you, and maybe be able to head in a slightly straighter line through your research. But even professors are not perfect in that regard. Until then, as @user37208 suggests in the comments, your advisor should be a great source of advice here and can help you to break down the problem into more manageable chunks, and give you a bit of direction when you feel you are wandering around without success.

You may be thinking "that's all very well, but at the end of the day, my thesis will pass or fail." While that's true, this will depend far more on how well you can explain what you have done, and whether you can demonstrate that you have made reasonable efforts to tackle one or more problems, than on whether you have actually found "an answer" or not.