Solid projectiles do travel a bit further than their specified range. energy based weapons stop right on the dot, though i'm not totally sure about PPCs
AFAIK all AC's have unlimited range, but with reduced damage when hitting something past their max range.
All Gauss weapons also seem to stop on the dot, like lasers.
PPCs travel a small bit beyond their max range I think, at least I vaguely recall hitting something out at 800m with a standard PPC, but I'm not totally sure...
1) What is the maximum range for LRMs?
simple answer: to frikin far.
Beyond 1000m you'll only be hit with LRMs if you're standing still, which you shouldn't be doing in the first place, unless you're missile boating too, in which case you should get some nuts.