How are "Alternatives" Legal?

Hahaha, it's, uh... complicated... IANAL, but my understanding is that there's case law that basically says that since software's not a tangible good, it's covered by copyright law like literary works. As such, there's nothing to stop someone else from writing a program that does what a proprietary software does (like writing another book in a genre), as long as they don't "plagiarize" (copy) the code. This is a very good thing, but probably best discussed in detail elsewhere by someone more familiar with the law (Eben Moglen's a well-known copyright lawyer specializing in software law, i linked to one of his talks below).

In any case, the examples you've listed are all examples of "Free Software", which is also commonly referred to as "Open Source", or "Copyleft": software that is made freely available in its source code form for inspection and modification, under a variety of licenses. For more information it's probably best to read it from the source. In particular, pay attention to those 4 enumerated freedoms, as they are super important to understanding why people spend so much time and energy on work that they then give away for free.

If you're interested in more, these are a couple of my favorite videos on the subject:

• Richard Stallman - Introduction to Free Software
• Eben Moglen - Freedom in the Cloud
• Corey Doctorow - the coming war on general-purpose computing

edit: I should add, Richard Stallman is a wonderful person, but he occasionally lacks some social graces. Despite this, he's been proven to be correct time and time again, and he's dedicated his life to helping protect people from malicious technology, so I tend to listen when he speaks, even if he may come off as a little strange sometimes :)