I would find it hard to believe that you can legally rebrand Audacity without violating the licensing.
Though you didn't asked for advice here but as a fellow member I'd request you to search on net or ask a lawyer first if its legal? You can add/modify GPL softwares but can not rebrand.
You can redistribute Open Source software under a different name no problem, it happens all the time but you must keep in the copyright notices of the original author/company
No problem rebranding the software at all. That is what many development forks do. Look at Joomla, it came from Mambo which came from something else. WordPress had a predecessor as well. Generally there is some sort of development when a fork happens, but not always right away. I am surprised many more enterprising types aren't into rebranding. Imagine rebranding a wordpress install as your own and then selling it off to a client as a custom built solution.
Yes but you would have to say that it is a customized version of wordpress otherwise you are breaching the wordrpess license. This is fact.
@ibizuk: so you say, but WordPress is released under a GNU Public License and it only requires that modifications have the same license. There is no requirements that says that new derivative work must reference the old work. If you keep it licensed under the same license, you are covered.
Exactly: make sure you read the license. Some software (e.g. Firefox) even force you to rebrand if you release a modified version. Also, it isn't particularly hard to rebrand: get a text editor out, search through the code, finished. The question though is why you would want to do this?
If you want to re-branding a program it is not have any issue, but you must include a notification regarding the original source.