Wat key is Dead Leaves and the Dirty Ground in?

My score is in 3 sharps - A Major. What I notice is there's no cadence in A, which is why you don't have the "coming to rest" feeling.

There are lots of accidentals in the music, as you've discovered through the G, C and F chords, and although no scales are used as such you'll find the A natural minor and A minor pentatonic with an added F# used as a passing note are fairly close to what Jack White's doing. The A, G, C, D, A progression in the pre-verse section could easily be V-IV in D, then the G, C, D bit could easily be I-IV-V in G and then D - A is an Amen cadence in A but it kicks off the next section, so who knows. The overall feel of the song is very restless.

Using dissonances like this, with minor scales against major chord progressions (which is what we use in blues), and increasing the chromatic interest with out-of-key chords is routine in rock music. Don't get too bound up in looking for normal chord families in a song.

Thanks for the answer. I did not understand what you meant in the beginning though with "My score is in 3 sharps - A Major" though. A major has 3 sharps, but I did not get what you really meant.

And also, if the scale would be A natural minor, then only the F#-chord he uses is an accidental, no?
But the overall answer is that there really isn't a clear-cut answer?
Makes me a bit sad because I'm trying to study a bit of music theory on my own, but often then there are no real answers as to why some (chords in) songs sound good and others do not.

I did not understand what you meant in the beginning though with "My score is in 3 sharps - A Major" though. .

I'm working from written down music - little black dots rather than internet tabs. The Key Signature on my music is 3 sharps, which means either A Major or F# minor. There is no E# in the music (leading note to F#) and my first chord is A, so I reckon I'm on fairly good ground saying it's in A.
And also, if the scale would be A natural minor, then only the F#-chord he uses is an accidental, no?

You're in the ballpark, but do not confuse scales and chords. There is an F# in the A melodic minor scale, and there is a chord of F#m in A Major.
... often then there are no real answers as to why some (chords in) songs sound good and others do not.

This can be down to luck, but the classic example is Hendrix's Hey Joe. the chord sequence is C, G, D, A, E.

No obvious connection? Wrong. It all proceeds in 5ths.

G is V of C
D is V of G
A is V of D
E is V of A

Keep up the theory studies. It pays dividends.

This is a classic case of "key of A Rock".

It's an ambiguous mixture of A major and A minor like a million other rock songs. It's related to A Mixolydian (but it's not really). It's closer to A minor with a major I chord.

One chord substition I Am -> I A does not really make a new key.