If your front derailleur is hitting the rear tire, it is either bent, or poorly adjusted. I would assume a derailleur angled that way would rub no matter what you do.
It also sounds like you are taking a shotgun approach to diagnosis (since you are adjusting H & L screws for rubbing, which should only be done if you are shifting too far and dropping off the chain rings. The shotgun approach can be useful at times when you can't easily determine a root cause, but a front derailleur is so simple that I think if you look at a video or web site dealing with installing and adjusting the FD, you should be able to get it working properly.
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