Quote Originally Posted by leo
to be able to is a kind of expression of ability and definitive declaration, I think, not "possibility or likelihood", right?
Correct. "may" and "to be able to" are different; e.g.,There's a likelihood/possibility that we will be able to help you.

Quote Originally Posted by leo
"You may apply for engineering technologist first, and leave it to the assessor to make a final decision." In which I think the "may" means "be permitted to", not "possibly can", right?
Correct, again. "You are permitted to ~ We give you permission to . . . ."

All the best.