These might be some silly questions, but...
B-string output: have you tried slightly raising the pickups on the B-string side? Depending on what strings you were previously using on that bass (ex: taperwound B), the pickup might be currently set a little too low.
G-string 'buzz/zing': Sounds like you might have to tweak your trussrod and/or action at the bridge saddle. Once again, depending on the gauges of your prior string set, some minor adjustments might have to be done.
If you have questions regarding setups, there are some good 'sticky' threads in the "setup & repair" forum.
Hope this helps. Good luck!
