I am in TPS as well as F1. My OPT is going to expire in june, but I do have option to renew my OPT. But my company also agreed to sponsor for H1B. And I am thinking to apply OPT at the end of next month. So can I submit my H1B application on april 1st when my OPT is still in the process? Any ideas will be appreciated

You can and You should. H1b denial are very common and if it happens, you can continue in your OPT. If somehow your H1B gets approved before OPT renewal, make sure you call USCIIS and cancel your application of OPT extension ( This is not necessary, but just to avoid issues where USCIS screws up and extend your OPT after h1b is already approved)

yes