Hi, I have a ESP Horizon FR-2... and I recently switched to Ernie Ball's 10-46 string gauge.

I'm having so much more trouble palm muting those open notes... I feel like the E-String is too loose.

How do I fix this? Could this be a result of too much bow?? Cause I fear the neck goes back a bit, as if it needs a truss adjustment.

I'm guessing you've dropped down some guages and your guitar was set up for a higher guage. If you know what you're doing adjust the truss rod, if not take it to a technician it's a simple fix.
Check the angle of your bridge, check your neck if it's straight or has too much bow to any direction. If all those are perfect or near that, then the strings are just too loose to your liking and you might want to get some bigger gauge strings. What tuning are you in? E standard?
Gear pics

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I'm in E standard, and on the contrary, I've started in 9, and went up to 10... should I take it to 11??

I'm pretty sure the neck has some backbow (i.e it goes back, as if the strings are not tough enough).. I checked it just like the manual said... my strings are pretty close to the frets.

So if I go up in gauge and adjust the rod so there's no bow at all.. would it fix the problem?

Sounds like you have what I have. A very heavy picking hand. In order to fix that, I had to start using Ernie Ball's Skinny Top, Heavy Bottom. Ever since, it's been a hell of a lot better.
That's not plausible cause I've been palm muting the hell of out of my last guitar, playing songs like All Nightmare Long quite perfectly, so I'm pretty sure it's not my picking hand.
And from what you're saying, the thicker the string, the easier it gets.. so it's the exact opposite for me, I'm used to .042 and went up to 0.046 now.

It's either the guitar with it's damned backbow (which I'm going to fix as soon as I get the right allen wrench......) or the strings... Just thought you guys might know which one exactly.