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'.
- 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.
"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.