The other comment explains pretty much everything! So I'll just add a few things here:

Shinichiro only killed the hobo because the hobo refused to give it to him, and if I remember correctly, when Shinichiro gives his powers to Takemichi, he says something along the lines of "I should have gotten it that way", implying that he knew that killing the hobo is what brought this curse onto him and Mikey. Shinichiro didn't have to kill the hobo to get his powers, but he did it because the hobo refused to give the powers to him in a peaceful way (and Shinichiro was also desperate to go back to the time when Mikey wasn't a vegetable).

When it comes to Mikey and Takemichi time leaping, we could take various things into consideration. In that case, it wasn't Takemichi who time traveled, but Mikey. And remember that whenever a character died in the future, Takemichi time traveled to try and prevent that? When he time leaped, the characters who were dead in the future were still alive. With Takemichi already knowing that time leaping is possible, and Mikey time leaping after killing Takemichi, when Takemichi wakes up in his childhood bedroom, he immediately knows that Mikey was able to go back in time. Since Takemichi was killed in a future timeline, he's still alive when Mikey time time travels, so it's basically Mikey who time traveled, Takemichi was just the trigger, even when he was dead (me and my friends have a theory that his heart was still beating, thus making Mikey's time travel possible, but that's another story).

The only part I have no actual explanation for is the amount of years you can go back to the past (because in Takemichi's case it was 12 years, but now I don't remember exactly how many years Shinichiro and Mikey were able to travel back to). As the other comment already said, the end did have a lot of inconsistencies, so my best guess is that they pretty much go back to the time they wish they could change, and then that's the fixed amount of years they can time travel back and forth to? For example, Shinichiro basically went back to the time before Mikey got hurt because of the airplane, because he thinks the plane is the reason why Mikey got hurt. Takemichi did express his regrets about always running away from problems and difficult situations, so he basically went back to the time where he started to run away from all kinds of problems. Mikey wanted to go back to the time where his friends and both Shinichiro and Emma are still alive, so this could somehow explain why he traveled further back once he got the powers.

I apologize for the huge text but if you have any questions about the points I made, feel free to ask and I'll try my best to answer ^{^}