#1
So i just got an LTD EC-401, and while i really like the neck and the general feel of the guitar, there are two things that bother me. First, the pickups are slanted. Not side to side, but they are angled towards the bridge, so the side closer to the neck is higher than the side closer to the bridge. Will replacing the springs in the pickup rings help with that? I actually managed to get the bridge pup level by just pressing down on it hard a few times, but the neck one is still a bit sideways, and its bugging me. Also, for some reason, the neck pickup ring isnt parallel to the strings, its lower on the bridge side. Could it be mounted wrong, and i just have to flip it around?

Second, the bridge simply falls of when i change strings. I only did it once, as soon as i got it, and it plays just fine. I checked the intonation pretty much constantly since then and it seems to be holding it pretty well. The action on the guitar is great, there is no fretbuzz, and all in all it plays really great, its just that when i change the strings the damn bridge will fall of again. And i am talking about the bridge, not the tailpiece or stopbar or whatever its called, although that one also wants to fall away, but it only gets away from one stud, while its still attached to the other. Again, when strings are on, the tension just keeps everything locked in place. Is this an actual issue, or is it just normal behaviour on TOM bridges? I vaguely remember having the same problems on an epi lp, but that was almost 5 years ago, so i dont really remember what happend there. I guess a bridge change would fix this problem anyway. Would THIS bridge for example, fit on the guitar? I guess i can just go ahead and measure.

Again, i have to say that this guitar plays awesomely, and i really dont want to send it back and risk getting one that plays worse, so i would really like to fix this issues myself.

Anyway thanks for your help
Joža je kul. On ma sirove z dodatki pa hambije.
#2
Normal behavior for TOM bridges, except for the ones that have a screw in the bridge that tightens to the post. Everyone deals with the TOM bridge falling off; I think, sometimes, that's why blue painter's tape was invented and/or why so many people change just one string at a time.

Don't go mashing down on the pickups to make them sit level. The middle screw on both pickup rings is for adjusting that particular side up or down. SOME pickups (Carvin, others) have three or even four screws there, and the extra screws help you angle the pickup to run parallel to the strings.

#3
As Ds said, TOM's are always like that, except for the locking ones he mentioned, of course. I can't speak to whether or not that particular bridge would be a drop in fit, but honestly I've never considered the TOM coming loose when the strings are off a problem...not enough to want to buy a new bridge at least. (Don't tip the guitar?) The tailpiece coming off has always annoyed me more.
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In my experience, pickups that are unintentionally slanted are usually caused by the wiring under the pickup pushing it in one direction or another, which is likely why pressing on it yielded some results. The only simple ways to fix that would be:
To take the pickup ring off and try to wrap the wires in a way that they do not interfere with the pickup, but usually if that's been happening, there's not much room to play with.

The other option would be snip the wires shorter and solder them...I wouldn't recommend that unless you're 1. absolutely sure you won't be using those pickups in a different guitar (that might need more wire) and 2. Confident in your soldering abilities/know basic wiring.

You could also try pulling some of the excess wire into the main pot(knob) cavity.
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Most pickup rings are slanted intentionally to match the neck angle on the guitar, if the neck pickup ring is high on the NECK side and low on the BRIDGE side...it's safe to say it's mounted wrong. Just unscrew the whole thing, detach the pickup from the ring, flip the ring and reattach the pickup (you want the pickup mounted the same way it already was, just flip the ring).
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While you have the rings/pickups out; to test that the springs/mounting brackets/etc are fine, just hold the unit in the air and see if the pickup is still slanting (not in the direction the ring itself is slanted, of course). It will probably be straight when there's no interference from the wires. If it is still crooked, then just inspect the unit and try to figure out what's causing it. With the ring mounting screws out, you can push it into place and let it loose, if the wires are interfering, it'l feel kind of springy and you'll notice the pickup itself going crooked as you push the ring into place.

Hope that was helpful!