First of all, although those two sentences do mean "How is it possible for me to improve my English?", that doesn't make them examples of modals of possibility/ probability like "That must/ may/ might/ could/ can't be John".
The difference between can and could in this kind of question is the same as the difference between will and would, and in both cases it is worth thinking of them, especially the past forms, as parts of conditional sentences. For example, "How will you react?" means "when you see him" but "How would you react?" means "if you saw him", even when that if-clause is unstated. In the same way "How could you improve your English?" means "if you wanted to/ if you needed to", whereas "How can you improve your English?" means in your present state of wanting to/ needing to. That't not a particularly important distinction in this case, but you might have a different level of shock depending on whether your friend asked "How can I kill my boss?" or "How could I kill my boss?"