A: Maybe, maybe not. If the buzz is persistent - i.e. doesn't go away when you touch the strings or gets louder - then you probably do.
If the buzz gets less when you touch the strings or any metal part then this is normal for many guitars, which is not to say that it can't be improved. You may need to invest in cavity screening.
Q: I plugged my guitar in and there's no sound coming out of it. How much will it cost to repair it?
A: It's impossible to say without seeing the guitar, but most electrical repairs on standard non-active circuitry can be done for less than £25, but I make no promises; sometimes it can take four minutes to fix the fault but four hours to find it. It's the four hours has to be paid for...
Bring it in but before you do check that the lead is working and the volume is turned up. No, seriously; you be surprised how often...