Cursed characters can return to the Town, but it'll be a rough journey from deep in the woods all the way to the Town when they're turning into a tree! It's very unlikely they will be able to make it all the way back before they turn into a tree completely.

They will still have awareness of what's going on around them yes. And damage to their tree-selves will translate to damage to their bodies as well -- it's up to you to decide if losing a branch is akin to just having a deep gash, or actually losing a finger, though!