My payments limit has been met and my forms are going to be disabled on Monday at 12pm. Will they be re-activated come the new month of June?

Since June is on Wednesday, will everything go back to normal? I'd really not like to pay for an upgrade at this time. 

Yes, on June 1st all you forms should be working fine again, all the counters will reset except the uploads counter and your account should be working fine on that date.