There is no law against playing another songwriters material.
Technically, you have to do is pay the ASCAP fee for the songs, but is usually covered under a blanket license the bar/venue already has. Not a big deal.
The look, well, most bands didn't design their own clothes (unless you're talking Kiss)
The logo can be tricky, and can be a point where infridgment can become an issue. Just make sure there is some difference in the bands name to make it distinctive enough from the original. There are so many tribute bands around the world these days, I don't think the average band is going to make much of an issue over what you are doing.
If go make a recording, then you have to make sure you have the music properly licensed, but even this isn't all that difficult.