No, 1 and 3 don't mean the same thing. The changes in the verb change the meaning.
1. He has gone. On its own, this means he has left recently and he hasn't returned yet. 'Can I speak to Gordon? Is he still there?' 'No, he has gone.' We often include the place as well: has gone home, has gone to work.
2. He is gone. People sometimes confuse he's [he has] with he's [he is] . In some places, He is gone is acceptable, especially in casual speech, but it isn't acceptable everywhere and should not be used in formal writing.
There is, or used to be, a slang use of gone, in which gone was an adjective. He is gone, man--but you probably have to be middle-aged like me to use it. :wink:
3. 3. He goes. We use verbs in this form to show things like habits, normal practice, routines or things that are generally or always true. This sentence seems incomplete on its own; we want to know where, for example. In speech, and sometimes in writing, though, we may understand that a word like home or out is meant but not actually said.