Yes, they can be used all together and this is routinely done all over classical music. Perhaps it's better to avoid using different flavours simultaneously in different voices (though even that is not unheard of), but switching back and forth between natural and harmonic is no problem at all.
Note that usually, the harmonic and melodic scales are most interesting in the ascending direction, because they contain the strong upwards leading tone ♯ⅶ, which pulls towards the tonic, creating a nice cadential phrase-conclusion effect.
Sometimes the melodic minor is also interesting in descending direction, amongst other things to avoid evoking any final character in the ♭Ⅵ-Ⅴ step (which also occurs in the dramatic ♯Ⅶ°⁷-ⅰ resolution) and to adapt for another voice that's already ascending in melodic-minor. But for the harmonic minor, these reasons don't apply, in fact the augmented ♯ⅶ-♭Ⅵ has quite a dramatic effect of its own right. Mind, precisely that effect is actively sought in some genres (e.g. Flamenco), but it's generally avoided in western classical music.
I did more of an in-depth discussion of the subject here.