Question

why some sentences begin with ....1. to my surprise 2. to be able to do it ......what grammatical aspect is it

Answer 1

"To my surprise" is a prepositional phrase. It's usually used adverbially to add emphasis and detail to the verb's action.

"To be able to ..." is an infinitive phrase. These are often used either as adjectives or adverbs, but I'd need to see whole sentences to know for sure.