[DALAZ_68]

Ur ''Stand by power" or Idle power sounds like an Alternator/old battery issue/batteryconnection issue

if the battery is new, then recheck it (it would'nt be the first time a brand new battery failed)
if ur battery is properly checked then next would be your Alternator, its old, it happens, rebuilds are around what 60 bucks, should rebuild it anyway,
if ur battery and alternator are good check ur connections to the battery, rust and other shit (loose terminals) can cause improper charge to the battery

since u said its only problematic during idle, id pretty much would not bother looking at the battery ( since the battery is only mainly used to start the car) and focus on the alternator and ground, all of these issues can be checked easily at Autozone,kragen,pepboys...etc for free...

ur bogging sounds like a MAF issue, when u get to higher RPMS its probably not registering air flow properly and bogs u out, clean it, theres spray cleaners specific for the maf, clean the plug aswell.

ur shaking sounds like ur eng and tranny mounts have gone to shit, no surprise, ur in chicago, ur cold ass weather and 18+ year old mounts, guess what, it kinda happens, just get some OEM replace ment from like Autozone, its like 100.00 for both engine mounts, i dont know if they have the tranny mount, or get nismo mounts, there a bit stiffer, but well worth it, thatll probably run you around 180 for all three, and there not at all hard to remove and install, 12 bolts in total.

GL

P.s.

might also wanna change ur Fuel filter, get a 90 300zx non turbo filter and slap it on.