Let's understand the plot!

Wasn't the priest the other young friend of Hyo Je and Ji Won? The one that talked with Hyo Je when Ji Won was cremated? That's what I gathered from it. Especially with that ending, when he brought Hyo Je to older Yeon Hee from the present time.

As for the 2nd: there is no beginning of that loop. That's often a problem with time travel movies and shows that I somehow learned to ignore. 

full movie short: there is door that connects all dimensions of different times every 25years which also involves disappeared people that went in into that door and never came back, they don't realize they disappear or died because they are still in their time. husband dies, kid disappears mom gets in prison after 25years come back to search for kid who she witnessed disappear. the door opens she gets in bam she is in loop that connects even past, she goes to find kid who disappears but it was him the alive one in past meanwhile the disappeared him went to look for his dead brother cuz he missed him. finally mother comes in contact with his disappeared son who is in older self I guess because of some story that he was in past (diff story it wasn't touched much and the kid was reincarnation so he was in his first form but still having presence memories) he explains the loop and tells her to go back to the his old old presence since he has smth to show but she is behind the door where her husband tried to kill the son, she decides to better go save him than go back to very past and she doesn't mind to begin this loop again. She goes in, accidentally kills husband, tells son to stay but as her young self called for her son she realizes something and takes the kid inside the loop only to come out quickly in present time. Since the kid has an illness and there was no medicine she brought him back to 25years later in case it was at least developed or being invented and he still has chance to live but since she is dying in that presence she left the kid to his past bestie who is now priest. the end,