Originally Posted by: UNCLE...do I play these chords separately or are they supposed to be combined in some way?

Gm Gm/F Gm/Eb Gm/D

As user light487 correctly states those are a type of "slash chord" in which the first letter is the chord "proper" and the second letter after the "slash" is the bass note.

I don't know that song or artist. So, I can't help with the rhythm. But this is one way to finger those chords:

E|--3--|--3--|--3--|--3--|--3--|
B|--3--|--3--|--3--|--3--|--3--|
G|--3--|--3--|--3--|--3--|--3--|
D|--5--|--3--|--1--|--0--|-----|
A|-----|-----|-----|-----|--5--|
E|-----|-----|-----|-----|-----|
Gm Gm/F Gm/Eb Gm/D or Gm/D

Hope this helps.