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Can someone please help with these?

What's the difference in X versus ## for double sharp?

Does double flat also have another symbol too?

When would you need a natural paired with a b/# together as one accidental? Would that be if the note before was a double sharp/flat? I assume this means the note is now natural then apply the the accidental thats paired with the natural? Or else you'd need a triple accidental.

No difference. The X symbol is more common, but I suppose sometimes you'd see two sharp symbols.

No. Accidentals don't have state. An accidental always indicates, by itself without reference to previous notation, the note to be played. Even if you have a double-flat, if you then have a sharp the note is sharp and that's the end of it.

All of the above are just alternate notation used in some older scores.

Makes sense! And wth was I thinking.... I'm not even sure why I even thought that as know how they work. I guess I was trying to come up with a made reason to use the odd looking natural plus #/b hahah. Thanks for the help!

There is something else going on with that example. When I first came across (nat)b and (nat)#, I was starting my studies of music theory. There were two alternatives given, the other being just a flat or sharp. My then-teacher explained that most scores don't have the natural in front (as per your example), but a few do. I think (?) he said that the combo version was an older convention, but I can't remember.

I suppose a different thinking went into both variants.
* (thinking 1) If your previous note was Abb, and then you have Ab, it's a brand new note - the Ab replacing the Abb as note. So you just write Ab (b in front of A, no natural sign).
* (thinking 2) If your previous note was Abb, moving the A down twice by two semitones, then one of the "move-downs" is cancelled via the accidental, which causes a "move back up" to your Ab. Someone thinking like that would write Ab as (nat. + 1 flat in front of A)

Since the time of that discussion long ago, I have hardly ever seen the variant in your example.

The Schubert Impromptu, Op. 90, No. 4 in A-flat, measure 25 (third measure in this example) :

In some editions the A-sharp is preceded by a courtesy natural sign as in this edition from Breitkopf und Härtel and in my (old) Henle. In the new Henle, there is no natural sign. This is the Breitkopf:



In some other editions the natural sign seems to have disappeared.

Regards,

Quoted from WIKI
"Double accidentals raise or lower the pitch of a note by two semitones,[4] an innovation developed as early as 1615.[citation needed] This applies to the written note, ignoring key signature. An F with a double sharp applied raises it a whole step so it is enharmonically equivalent to a G.

Usage varies on how to notate the situation in which a note with a double sharp (or flat) is followed in the same measure by a note with a single sharp (or flat). Some publications simply use the single accidental for the latter note, whereas others use a combination of a natural and a sharp (shown below), with the natural being understood to apply to only the second sharp. "


And it's use


Whole Article
WIKI

My ancient ABRSM edition (ed. Franck Merrick, bought when I was a teenager about a century ago) has no courtesy natural sign.