I think there are three questions at essence here.
1. What constitutes a good problem?
A: Every problem/question includes its own answer. This is very helpful to realize. There's a principle by which the world operates. The principle of the world means that results are determined by problems of what happened. In fact, if you open your eyes to this principle, it will also be possible for to see the answer in any question without having actually learned that subject before. The quality of the answer we can get from a question depends on the quality of the question itself. Good questions are substantial, concrete, and precise. They contain matters, which can be confirmed. So, once this is understood, we can see that a good problem is simply one which has a good result/outcome/answer. You should know what result you want in order to check if your existing problems have results which match what you want.
2. How to distinguish good from bad?
A: What are the criteria of good and bad? According to what I have learned, the more genuine something is, the better it is. For people, a person can only be a good person if they are truthful. Going to school, we might have different scores in different subjects, e.g. an A in English, a B in math, and a C in physics. But human beings are different. Every characteristic of an individual keeps up with every other characteristic within them. Would you suppose that it's possible for a person to be wise and yet not true? True and yet not conscionable? How about true but not courageous? To have a large amount of (bad) karma and yet be true? All the features of something which is good or bad are determined by degree of truthfulness. Incidentally, it's only possible to become more truthful after you undergo a particular essential process of learning by which you first realize that you don't actually perceive anything as it is, and later, after things that exist become visible to your eyes, you finally come to be able to speak about things that you really know. Generally, it's only possible to undergo this process when you meet and make yourself learn continuously from a truthful teacher. But undergoing this process is necessary in order to become someone who can be contributive to oneself and others. That is to say, we don't have the ability to guide our own lives contributively until we perceive what exists. What exists itself must be the standard for any judgement which is to be appropriate and contributive to existing circumstances. It's impossible to see what exists without truthfulness.
3. How are questions/problems themselves formulated?
A: Quite simply, any problem is made by putting at least two things into contact. For (contrived) example, let's say I have some things that I have kept inside my consciousness from the past (causes), represented by the numeral 2. Let's suppose I meet a teacher, who could be represented as the numeral 3. The result/effect I'll naturally come to gain through the process which is determined by the factors in the problem will be 5. You can make problems that you need in order to get results you want by fixing (i) the causes you have in you at the moment, and (ii) the result you want, and algebraically solving for the cause you need to contact. In order to contact a cause you need you either need to find out how to form it through existent things, or you need to find it among what exists and go there. As mentioned, one of the real problems that general people face is that they can't see the causes they have in themselves.
Does that help?