Have you seen the final ep? Not yet? Then Don't read this..
SPOILERS! SPOILERS! SPOILERS!
I believe the ending was meant for Sun Woo to go back to the past to save the 2013 Sun Woo (he was heading to Nepal). He was deemed to help the 2013 Sun Woo because he knew he died. As for Min Young and other things,.,as he said, he will simply believe in himself and the choices he will make, and love who he wants to love.
What was bugging me here was why would Jung Woo go again to Nepal to find the incense sticks if the tragic family thing was straightened by 2013 Sun Woo? And yeah, Sun Woo the 2nd was supposed to follow him. Memories remain right? Maybe Jung Woo really felt bad on what happened to his brother, so he went back to Nepal to find the sticks, also to attempt to save the 2013 Sun Woo. Sun Woo the 2nd will attempt to help his brother because he knew he was going to die and the cycle on the first Sun Woo will occur again.
I rewatched the first episode and it is a flashback on the last few minutes of the final episode. Jung Woo saw a man, then it was cut. No time frame was said; what if it was a time loop from the 2nd Sun Woo?....Did that mean Sun Woo the 2nd succeeds in finding his brother , and since he knew about the cause and effect the sticks can give, he will prevent the brother on finding them., thus everything will go back to its rightful place just before the existence of the incense stick. **pulls hair due to confusion**
EDIT: Another thought: On the last minutes of the final ep: Sun Woo said : " It's been a long time, Brother."- means he didn't saw Jung Woo until that day (as opposed to their recent meeting on Christmas day on 20th ep) Does that mean the 2nd Sun Woo finds a way then was able to save the 2013 Sun Woo from 1993 death?
Edit2: I found this one on soompi and I thought it made sense. Sun Woo the 2nd was planning to go back to Nepal because he knew his brother was going there. The reason? Jung Woo wants to save his father because he died on accident. Sun Woo found his brother dead before he arrived. He waited for 20 years to save him., then he was finally able to see him (the last minutes of the final ep) and prevent him from dying again.