Hello,

Whenever I play some shred, I tend to push down the tremolo with my wrist, which pulls the strings and makes it sound out of tune. I have installed a tremol-no in it, which blocks the tremolo, so I can have my wrist push down on the bridge when shredding.
I've tried to move my hands away from it, but it feels so unnatural and I can't play as clean and fast when I do it like that. Secondly, I think my hands are too big not to have my wrist at the tremolo.

Where is your wrist when you're alternate picking?

My wrist is resting on the bridge, the edge zero, of my Ibanezes. Sure if you push too hard it becomes out of tune, but that's the case with the fingers on the fretboard board as well. It's all a balance, and I reckon you can tough your tremolo lighter than you do, if the case is that it goes out of tune. You shouldn't be pushing down on it.

This is just a guess, but given that you're pushing down on the bridge, it sounds like you might not be relaxed with your picking hand?

These are usually related on how you balance the guitar. Like if the guitar is on the right angle on you lap or body or if you're trying to get the balance with your wrist instead of arm.

If you push down the tremolo with your wrist, definitely you don't use good resting points for your right hand. Maybe your hand is resting of the surface of the guitar body and this is not a good thing.
The right hand should resting always in two points, the edge of the guitar (which is the main resting point) and the side of the right hand on the bridge.
All the force of your right hand should be on the edge of the guitar not on the bridge. You touch the bridge but you should have no pressure there because your hand it rest on the edge of the guitar. In this way your bridge issue will never happen
Also your right hand should not be totally straight on the bridge, should be a little angled. You must use a wrist motion not a forearm motion. In this way your right hand will feel natural no matter where is the spot where you want to play (near or away from bridge).

Well, sometimes I tend to get a little tight and flexed when playing something challenging. But even if it's just a little, it still gets out of tune. My hand can only barely touch the tremolo without going out of tune. It's on my Ibanez S-520. Does yours do that too?

You should be able to "rest mute" on the bridge without pushing it out of tune. You may be resting/muting with too much force. Try to lighten it a bit and keep your hand loose. this will also help your picking

Todd