I understand that some of the aspects of the gameplay are confusing or hard to deal with, but I'm pretty sure most of these are accurate to the arcade original.
As for the branch hit detetcion, you kind of just have to get a feel for where it's going to hit you (if there's one pixel of space between Yosaku and a branch, you're probably safe). The tree hitting position is also accurate, and was never an issue for me, then again I got used to it, and think it adds to the challenge. As for the boar, it's worth keeping in mind that it will always appear about four seconds after you completely chop down a tree, so after you do so, try to avoid hanging out on the right side of the screen so you can more easily avoid or hit it. For dying when walking into branches from the side, they probably still hit the top 8 pixels of Yosaku's sprite. It doesn't work no matter what, only if they visibly don't hit his head.