Key to learning algebra? I think it depends on what you mean by algebra. To me, algebra is just arithmetic where we're allowed to use symbols that aren't exactly numbers (variables), or represent numbers that are difficult to write (e.g. $\sqrt{2}$ and $\pi$.) I say "just arithmetic" because all of the old operations and distribution works exactly the same way. I have found many students struggle because they never even mastered the basic arithmetic rules. I think if they did, doing it with $x$'s would make no difference.
Incredibly basic exercises I obviously have no idea what's going on in your head about these exercises, maybe you're exactly right in all or some of your thinking about algebra problems. The problem with this is that this isn't useful to anyone unless you can write it down.
I'm not saying you are this type of student, but I have seen some students fall to a sort of overconfidence where they think they understand something, but it's clear they don't, because their work and answers are completely wrong. The only antidote for this is practice and validation of your answers. The clearer your written solutions are, the clearer it will be in your mind.
Memorization Memorization is an extremely blunt tool, and yet many students treat it as their main weapon. Memorization is too often used to avoid or delay thinking about things that really ought to be understood. My wife would say I have an awful memory, so I can probably attest that math is not so much about memory.
Certainly there are some things that need to be memorized, and there is no sense in spending time "understanding" them, like adding and multiplying single digit numbers. The quadratic formula on the other hand is a borderline case that is good to have memorized, but it's also good to understand where it comes from (completing the square on a quadratic equation!).
Contrary to popular belief, we use mathematics to simplify problems. I would casually argue that a core tenet of math is: "You just find the right way to look at it (or represent it) so it becomes simple".
Edit Dejan Govc inspired another thought with his comment about a student being uncomfortable with what exactly a variable is. This is true: it makes people uncomfortable when something new/ambiguous is introduced, like this. This is because the student hasn't "made the jump" to that new way of thinking yet. Being able to make these jumps is important, because as they learn to abstract further, they will encounter this feeling of disorientation all the time. The best thing to do is simply admit to yourself that you don't get it totally, but trust that through practice you will finally gain a feel for the idea.
If you were to advance in Pure Mathematics, you would also find that the theorems get more technical, with all kinds of messy hypotheses. What you are seeing in Pure Mathematics are results from a century or so ago. Many books have been written about them, and the has been a lot of time to clean up the results and proofs.
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Well I truly started learning and memorizing mathematics when I started listening to how Fields medalists talk about their work. Basically these guys are doing mathematics which most of us are never going to be able to understand, but when they talk about it, it all makes sense and is it graspable what they are talking about. The point being is that behind most of mathematics there is a way to truly understand what is going on. You must not allow yourself to get bogged-down in formalism.
What works best for me is to make notes when I am stuck. If I find a proof which is not quite clear to me I try to isolate which part does not make sense, and then follow the steps until it starts to make sense. When it starts making sense I try to think where else would such a thing make sense. When I am swimming in clear waters again I try to isolate the point of the proof, and method it used. Lastly I write down all definitions and theorems in spaced-repetition system, because "repetitio est mater studiorum" as they used to say.
Lastly what I find useful to do is find a book and stick with it. I learned to not change literature often, because in every book there is going to be part where you are just hopelessly stuck. When you are stuck, come back here and ask for help. With these steps you should be well on your way.