Can I mix the natural and harmonic minor scales in the same song?
Yes. It's helpful to think of "minor" as a collection of options rather than a single scale you have to commit to. Natural minor (Aeolian) is the "true" minor according to the key signature, and Harmonic minor and Melodic minor are representations of how composers modify Natural minor in their music.
So when you write "in minor", the "scale" available to you looks like this:
T:A minor note choices
"_1"A, "_2"B, "_b3"C "_4"D "_5"E "_b6"F "_6"^F "_b7"G "_7"^G A
A related question, with a related answer, came up here:
What scale is used with this descending bassline progression?
Can I play G, when a G#° chord is played?
Again, yes. It will be quite dissonant, but if that's the sound you want at a certain moment of the piece, then there's no reason to avoid it. As mentioned by @user1079505, you can think of G as Fx -- the #9 in an E7#9 chord. From that point of view, the voicing that will likely work best (with deference to your tastes as the composer) will be to put the G# below the D, and G (Fx) above.
In this example, the various options for B are given in parentheses.
T:Voicing G#dim against G
%%score (V1 V2 V3 V4 V5 V6)