#1
Could the tom bridge be the source of strings ringing wierd and intonation issues? What could be the signs and what could be the solutions?

would replacing the tom bridge with a new/better one do any good.
----------------------------------------------------------------------------
-Jackson Soloist Std. Professional '93
DiMarzio Evolution (bridge) SD Lil' Screamin Demon (neck)

-B.C. Rich Warlock Special Edition Metal Web

-Peavey Bandit 112
#2
String intonation yes..
Strings ringing weird.. Is just a bit too vague..
#5
Guitar? Age? Fretboard condition? Boobs?
Epiphone Les Paul Standard Plus
Jackson King V
Jackson Kelly
Handmade Gibson Les Paul
Marshall JCM2000 DSL100/JCM900 1960 Lead cab