Re Every Rose, I play it as you wrote it above. That's a C add 9. The third fret on the b string is a D, which is the 9 you're adding. Regarding the Dm7/G, your voicing is correct! How it sounds depends upon how you use the chord. In fact, a lot of chords change texture depending upon how they're used.
Example: My band plays a lot of blues-based rock and funky stuff. Our bass player is really active so I don't have to play full chords. I mostly play thirds, sevenths, ninths, and other chord extensions and let him handle the bass note. He can move from bass note to bass note and change the chord without me changing any notes at all, or more frequently with me just changing one note.
To hear an easy example of how this sounds, play this:
x
5
5
5
x
x
That probably sounds like C major to you. So put the C in the root to define the chord as C Major:
x
5
5
5
3
x
Now play this:
x
5
5
5
x
5
That's an A minor 7...which from theory you know is the relative minor of C. The point being you don't have to change notes to change chords. Cool, but motion to a relative minor being a bit too easy, let's do a tougher one.
I play this in Use Me by Bill Withers (chord tone names added for reference):
Em7
x
12 (5)
12 (b3)
12 (b7)
x
x
A7 (with a 9 added for fun):
x
12 (9)
12 (b7)
11 (3)
x
x
So just by changing one note I go from Em to A7, which is a i-IV progression.