If I could fix my car, I could drive to the city.   And if  I could drive to the city, I could find some parties!

And of course, the Conditional in the past means it is TOO LATE.
(S + COULD HAVE+ V3 + [then] S + COULD HAVE + V3)
If I could have studied more, I could have passed the tests.

MUST

You will hear or see MUST occasionally in the Conditional, but usually it is in the IF clause.
(IF + S + MUST + V1 [then] S + MUST + V1)
If I must face lions, I must use a large gun. 

However, for must in the past, you would say "should have" as in:  I should have studied.

There is a time to say must in the Past Perfect Continuous, but (sit down), there it means a probability higher than might. As in:
I must have been sleeping when he left.

MAY

Usually the conditionals MAY, MIGHT, and MIGHT HAVE, are not used in the IF clause, but as a result of what happens in the IF clause. MAY and MIGHT are often used as degrees of conditionality, with MAY being of greater probability than MIGHT in the future.
Future:
If you are nice to me, I may invite you to my house.  OR
If you are nice to me, I might invite you to my house.

The conditional past is in fact the present. What is now might have been different (if you had been nicer....:)

Past:
If you had been nice to me, I might have invited you to my house.

You will be glad to know that these have been changing with modern usage. The main thing is for you to be aware: If the talk slips into the Conditional, you mustn't record it yet as fact.

End of Lesson W