Hey, so I have been playing for a few months now and I have a few questions that I need answered that I think would help me out alot.

I am having some troubles with this part of a song:


Now should I be palm muting the ADG chords since the D chord is muted, or should I just place my free fret finger on the D chord but not press down hard?

And lastly when I play anything in general the chords seem to ring longer then I want and in turn the sound is taking away from the next note I strum. Is there a basic technique that(such as resting my palm on the bridge after each note) to get a cleaner sound?

Thanks again, I am a beginner and any help would be greatly appreciated!
just have your index finger slightly over the D string to mute it.
My Gear:
Jay Turser Warlock
Baraccuda Strat
Takamine EG523SC
Samick Acoustic
Vox AD50VT
Boss DS-1
Boss CS-3
Dunlop Crybaby Wah