Okay, so numerous songs i've tried to learn I couldn't, because i can't play a certain part. Some of these songs include As Blood Runs Black - In Dying Days, and As I Lay Dying - Nothing Left. I'm not sure if it's the shitty tone of my Spider IV 15 or not, but I cannot play the parts that Alternate between a fretted note on the A string and an open palm-muted E. When I try to play them, the noise of the open E overpowers the upcoming note on the A and it sounds just terrible. I usually alternate pick these parts, hitting the A with a downstroke and the E with an upstroke. Can anybody give me any advice on how to approach parts like these (if you know what I am talking about)? Thanks in advance.
Downstroke the E, upstroke the A (ie outside pick). Might help.

Also, make sure you are properly muting the E string, so it doesnt ring out after being struck
ProTone Pedals: Attack Overdrive
Fractal Audio: AxeFX 2
Engl: Fireball 60
Zilla: Fatboy 2x12
Carvin: DC700
Carvin: Vader 7
Schecter: KM-7 MKii
Schecter: Banshee 8 Passive
Jackson: DK2M
Are you sure you are palm muting correctly? Maybe you removing your hand to play the A string note makes some noise? What I do (i have no idea if this is proper but i know it works) is hold my hand on the muted string the whole time. Idk if this is easy or hard for you since i also hold the pick like james hetfield and jeff hanneman.(three fingers)
Like they said down pick the open e an up pick the a, make sure you are muting the open e as well and make sure your in the right tuning as well.