I ask a lot of questions, but I should ask fewer. I'm asking him when I should be asking her. I asked him yesterday when I should have asked him today. I was asking only a few questions when I should have been asking a lot more. Clear?

Hello Tiuplan, No, 'should ask' and 'should be asking' are not identical obviously in their tense and in their sense as well. ' should ask' means it is good and preferable that I ask in the future ,near or far. 'should be asking' refers to the importance and preference of doing the action at the present 'now'. Examples: - The teacher asked to submit the assignment in 3 weeks, I should finish it soon. - I have to submit my paper work tomorrow. I should be finishing it today. "should have asked" and "should have been asking" are not the same as well. "should have asked" means it would have been important to do this action in the past, while now it is too late. " You should have called me earlier, now I can't help you." "should have been asking" is not a proper form to use, because "should have been doing something..." refers to the importance of doing that thing in the past in a continuous period or mode, while this doesn't suit the action of 'asking' usually, unless it is a peculiar context as in: "You should have been asking her again and again." Here it is asking someone in the past on a continuous basis. "You should have asked her . indicates that doing the action (asking) once in the past was important. Another example: "He should have been attending all the lectures at that time." It means he had to attend those lectures on a continuous basis in the past, it indicates repetition and continuity.

"I should have asked..." means I did not ask, but I wish I had asked. "I should have been asking... " is not the same thing. It would only be used in an unusual statement like, "I should have been asking questions instead of making assumptions" (or something like that). In fact, it's very difficult to imagine a situation where you would use a structure like that. "I should ask..." isn't really the same as "I should be asking... " either. "I should ask..." means I need to ask someone something; "I should be asking... " means I should be asking instead of doing something else (guessing? worrying?). Again, not a very common usage.

Modal verbs cannot express completed actions. They have no perfective aspect. (совершенний вид) So in none of your short sentences is anything actually accomplished. The auxiliary verb "should" expresses advisability or obligation. The meaning is only hypothetical. The speaker never actually asked....he only should have asked or should have been asking. When you use the modal auxiliary ‘should’ with a past tense meaning you add the-- 1) present perfect infinitive of the main verb.......have asked or 2) present perfect continuous infinitive ................have been asking. The difference is not in the basic meaning but in the emphasis. Example 1) My car broke down because all the oil leaked out. I should have asked my mechanic to check the oil. The present perfect infinitive emphasizes the ACTION of the verb in the indefinite past. You should have asked the mechanic during the time up to and including the theoretical moment of asking. 2) My car broke down because all the oil leaked out. I should have been asking my mechanic to check the oil. The present perfect continuous infinitive emphasizes not just the ACTION but also the PROCESS, i.e., the amount of time up to, including, and perhaps even continuing after the theoretical moment of asking.