Hi Mengha,

you're the only one who can answer most of those questions, but maybe that highlights something that you could work on. It is good to ask questions when you need to, but it is also important not to always rely on others to point you in the right direction. It is often good to figure out an approach to a problem for yourself, then follow it until you get the answer or realize that your approach doesn't work. Part of mathematics is about exploring ideas.

My only other piece of advice is to work on things in mathematics that you find interesting. There is no point in me telling you that topology is vitally important if it is not something that interests you -- do what you enjoy and you'll get more out of it.

Well, I can't give you directions, because I don't know where you want to go, or where you're coming from. But, once you get there, you can stay sharp by keeping your learning materials, and committing to doing a problem or two every few weeks. That way, it is always sharp in your mind. Also try to find situations where using those skills are practical. The more you use it, the more it will stick. The wider range of situations you encounter, the better you will understand the prinicples.