The short answer is "Yes". There are lots of organisations with publically accessable Confluence sites out there, and some of them are using modified source code.
For exact details of what you can do, you should get a proper lawyer to look at the licence agreement alongside the details of everything you actually want to do with it. But I don't think you've mentioned anything you can not do. I do know that you should not remove part of the footer that says "powered by Atlassian Confluence", but I don't think there's much esle you can't customise.
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