Visa validity : Exit re-entry query (very important)

Theoretically yes.  I have done it many times before without any issues.  However, check with your PRO as rules keep changing here.

You mean to say with people from the organization to which I belong?

The people who sponsored your visa.  Their PRO or government relations officer.

I spoke to a person who is responsible for these matters at sponsoring organization, He advised to enter before 28 April, However for me it is very difficult to come back before 28. Latest I can re-enter on 28th April. Hence I needed to just confirm from someone who has either practically faced such situation or knows about it well to get the comfort for entering on 28th.

Since You have done the same earlier and as per immigration system visa is valid till 29th So I feel it would be fine to enter on 28th.

Yes I have done it many times up till mid 2018.  After that I got my Iqama.  I have stayed beyond visa expiry date for sure - never for a full month though because I always come back to Bahrain on the weekend.