Answer: These terms: "natural," "harmonic," and "melodic" minor, are a little misleading, I think. Really there's just one minor, but it is more variable than the major mode. That is, one is more likely in minor to run into situations where altering a scale pitch seems like a good idea. The three terms refer to the motives for changing those pitches.

For example, a natural minor tune would have no accidentals (marked sharps or flats) outside its key signature. Here's one in D minor:

If we add some chords to that you'll see that we aren't able to use an "authentic" cadence, the strongest type (V- I or V-i), because that would require a C# in this key and the C is natural. So we use a VII chord (the major chord built on the seventh degree in natural minor, which is C in this key), and that gives this a sort of modal folk-like quality:

Suppose we really want the harmonic effect of the authentic V-i cadence? To do that we have to raise the C to C#. But not necessarily everywhere - only when we want that V chord (which is A major in this key of D minor). When we alter the seventh degree that way the result is "harmonic minor:"

But suppose we raised the C in a place where Bb came just before, like this:

Where you see the * we've created a melodic augmented second by moving directly from Bb, the sixth degree of the scale, to C#, the seventh degree. That's a nice sound, but a little exotic, and when composers wanted to avoid it they would raise the sixth degree too, making that an ordinary major second. In this key it would become B natural to C#:

So we've raised the sixth degree for a melodic reason, to avoid an augmented second, and that's the "melodic minor." Elsewhere in the tune the Bb is moving downward and there's no need to raise it - that's why it is said that the melodic minor has an ascending form and a descending one. So the 6th and 7th degrees of the minor scale are variable, and what you do with them determines whether you're technically using "natural," "harmonic," or "melodic" minor.

You mention unusual chords. If you want to harmonize that B natural with a chord that includes it, rather than as a dissonance as I did above, then you have the option of using a major IV or IV7, or a diminished chord whose root is the raised 6th degree, or perhaps a minor ii chord. That is, you simply consider as possibilities all those chords that would include the modified note. The ii chord would be diminished in natural minor, but the "melodic" form of minor suggests an ordinary minor ii. In this key the ii would be E,G,Bb until we raise that B to make melodic minor - that changes it to E,G,B, an ordinary minor chord that makes a strong root progression (rising fourth) to the A chord:

Minor keys are lots of fun to work with, and even when writing in major you may want to borrow from the minor at times.