1. They decide to leave the US on 4/10/2018, with application still pending with USCIS
a. Will this be considered as abandonment of application
It will not, the USCIS still wants to know/investigate whether or not you got a genuine reason for extension.
b. Do CBP/airport officials inform USCIS about the person leaving the country that triggers them to stop the processing
So, your application will still be processed.
c. Or, will the application continue to be processed and a decision communicated in the current time-frame, that is around May/Jun 2018
i. If it gets approved in May/Jun, then we are good.
ii. If it gets rejected in May/Jun, will they accrue an overstay for 2 months from Feb 21 to Apr 10, 2018, which puts them in risk of coming back the next time?
If it gets rejected for whatever reason, they will have already incurred two months of overstay. While this may be overlooked upon their future entries (since the case had been pending), this is definitely a flag!
2. They decide to leave the US on 4/10/2018, application is approved on March 21, 2018:
a. Will they still accrue an overstay for 1 months from Feb 21 to Mar 21, 2018,, which puts them in risk of coming back the next time?
Not at all. Been there done that!
3. They decide to leave the US on 4/10/2018, application is rejected on March 10, 2018:
a. Should they should leave the US the same day they see the update online or should they wait until they obtain the notice in the mail.
b. Will they accrue an overstay for 20 days from Feb 21 to Mar 10, 2018, which puts them in risk of coming back the next time?
They will have to leave the country immediately. And again, they will have already incurred an overstay of however many days.
4. We are in now on Jan 18, 2018. Their application to extend to April 10 gets rejected on Jan 21, 2018:
a. As long as they leave the US before the current Feb 21, 2018, they should be good with USCIS/Immigration compliance correct?
b. The rejection does not impact their existing I-94 expiry, correct ? (this maybe a stupid question, but just wanted to be sure)
No impact whatsoever.
Based on my own experiences, if you have a strong and genuine reason for your parents to extend their stay, I would not worry about getting a rejection. Good luck!