The purpose of the word “to” in that headline is to further reveal the subject’s (Floyd Mayweather’s) intention or to provide to the reader why it was given. Thus, the answer to (a) is yes, adding the words “in order” to the headline would be an appropriate way of rewriting it. However, it should be noted this is not a complete sentence (something that is common in writing headlines). In copywriting, headlines are usually quick, attention-grabbing snippets that have evolved from the days when printers would charge per letter and aim solely to convey the message as briefly and enticingly as possible. This can involve paying little mind to grammar. A complete sentence that conveys the same idea would be along the lines of “Floyd Mayweather gave a waitress a secret $10,000 tip to help her change her life”. You can see that the headline writing style does away with the preposition “a” and doesn’t bother with the Subject-Verb-Object structure, rather just a caption-like description of what the article is about.
As for (b), the first headline you wrote is not grammatically correct, “for helping waitress” does not work. If you wished to write it in that manner perhaps a better way would be “...tip to waitress to help change her life” or “...for waitress”. Once again, these are headlines and complete sentence structure and grammar come second to how they fit on the page and how they grab the reader’s attention. The second sentence you’ve written does not convey the same meaning as the original headline either, I would argue. As I mentioned above, the headline deals more with the intention behind why the tip was given rather than stating certainly the result of it being given.
Overall, it’s a bit tricky to deal with English through headlines like this as it’s almost its own vernacular.