Although some people believe that the use of a split infinitive as in "... to always do ..." is incorrect English, it is used in some texts as well as in spoken language. Nevertheless, I think using the adverb "always" is not appropriate in this sentence as the context is about the final exam this year which is a particular aim, not a continuous one. So my suggestion goes as: "To pass the final examination this year, Peter has to make every effort to do his best."

'always' needs to be removed - the sentence is confusing with it. "To pass the final examination, Peter has to make every effort to do his best this year." Not necessary, but personally I would make a small change at the beginning of the sentence. "In order to pass the final examination, Peter has to make every effort to do his best this year" or "So he can pass the final examination, Peter has to make every effort to do his best this year" This is just a suggestion, it's not necessary.

No