1. How do your parents allow you to ramble on in such an inane manner?
    What is the meaning of this question?
    Can you replace ramble with the equivalent other word?
  2. How do your parents allow you to wander off in such an inane manner?
    Is this sentence meaningful?
    Does its meaning equal to #1?

“ramble on” means to talk (or write) at length in a disorganised or confused way.

“wander off” can mean to drift away from the point of what one is saying, so #2 could potentially have a similar meaning to #1, though to me it does not seem such a likely thing to say, and “inane” also seems a better fit with “ramble on” than with “wander off”.

Babble or blather could substitute for “ramble on”. Chatter could as well.

“Don’t wander off on streets but sit and study since your exam is approaching.”
Is this sentence OK and meaningful?

I do hope you aren’t confusing to sit (to be seated) with ‘sit an exam’ is found in another of your messages.

Don’t wander around the streets but stay in and study, as your exam is approaching.