Getting a PhD would help (at least half a decade of wrestling with uncertainty will cure you of your fear of it), but I think an MEng is less helpful (I talk to a lot of MEng students who are working on some project where they are really over their heads.)

Then there are side projects. A good side project pushes really hard against uncertainty in at least one direction but is conservative in other respects. Being responsible end-to-end for a project forces you to confront things you might otherwise flinch at.

> Is it just applying past experiences to a new situation, or can you learn to look for solutions?

You can achieve anything you put your mind to. It took me a while to realize this. Turns out the brain is a marvelous machine and once it has a goal (solve such and such a problem) it will try everything in its power to solve it, since it's a goal-oriented machine. People doubt their own capabilities, and don't believe in themselves, which is their own downfall.