Can Someone Explain The Ending Of The Movie, Please? ><

After finished watching the movie and the whole series, I can't help but wonder a lot of things. One of the questions I've been stressing myself with is, why did Mai-san didn't know who Makinohara was? And how did Sakuto recognized Makinohara?

Did Sakuto actually went back to the past to 'save Makinohara' & Mai?

And how did Makinohara recognized Sakuto as well at the beach?

I really need your help. I'd really appreciate if you could answer this question with detailed informations, Thanks!