Yes it is but:
when speaking about medical things operation usually means surgery so it is a little strange saying surgical operation. Surgical procedure is better.
These sentences have the same meaning:
I'm going to have surgery on Monday.
I'm going to have an operation on Monday.
I'm going to have a surgical procedure on Monday.
it is not correct English, you rather say still
It is correct.
It would be more correct to say, someone who.
It is correct English to say decent skill but not decent ability
It is correct English to say "He went off on a tangent".
no it is not correct to say you are not for sure instead you can say in proper English that you are not sure about something
No. In English we say "How old are you?"
Yes, it is correct to say out of compliance with. It means out of help with in English grammar.
No, it is not proper English to say "on tomorrow." The correct phrase is "tomorrow."
no you should say "Did you get an A on the English exam?"
In American English we say My family is; in British English we may say My family are.
Certainly it is correct English to say, "She likes lingering in libraries." The alliteration makes it sound rather poetic.