Key of Eb

Main Prog
6 - 1(5bass) - 2 - (4 - 5of6)

Chords would be:

Cm - Eb/Bb - Fm - (Ab - G7)

The final G7 being the 5 of 6, however it is being played with the 3rd in the bass, so G7/B. Because of this, it also feels like Bdim during this moment, which makes sense as Bdim is the connected diminished to G7 (and literally inside G7)

There is also a line that starts around 0:47 that ends with a G7b2 type melody.

Key of E

Intro/Verse
1 - 1(3bass) - 6 - 4

Chorus
1 - 5of6 - 6 - 4
(minor 4 during the softer choruses, normal 4 during the bigger choruses it seems.)

Chorus chords would be:
E - G#7 - C#m - A

Could easily play any spicy dominant voicing on that G#, so:

G#(b9) or really G# with a b2
G#(#9) or really G# with a b3
G#(#5) or really G# with a b6

Or move the G# (the root) up a halfstep to unlock the connected diminished, which would be:

A or C or D# or F# diminished

Good example of taking a 1-5-6-4 and adding a tiny bit of spice by removing the 5 and replacing it with a 5of6. Also worth noting that she is often singing the same three notes throughout the chorus, 3-2-1 of the key or G#-F#-E. Over the G#7 (the 5of6) those notes would be 1-b7-b6, so a voicing with a b6 would probably sound the smoothest as the b6 is built into the melody. 

Key of E

Intro/Verse
1-5-6-4

Root and 5th of key are ringing pretty much the whole time, making certain chords have specific voicings. Like a sus 5 chord, min7 6 chord, sus 4 chord (with a little #4 at the end)

Chorus
6 - 4 - 1 - (5-5of6)

The classic move of taking a 1-5-6-4 (verse progression) and doing the literal same thing, but starting on 6, so 6-4-1-5. However they are doing a quick 5of6 right before the progression restarts with 6. They are also playing the 5of6 as an inverted power chord (3bass, just 3rd-Root) to achieve this chord.