Doesn't sound all that serious, if your not up to speed on auto electrics give it a miss and contact an autoelectician.
Other wise check both door switches are their! these are in the door catch (body side) also make sure the catch has a good earth to body.
Buzzing radio can be sorted out by a battery choke(fits on the alternator) go to maplin or auto factors.
maplin also do a gadget to test remote frequency output. some dealers have something similar too.(not just toyota)
Not to sure about the door lock light bit maybe its related to the interior light fault or faulty alarm.
Process of elimination is the best way...start simple! check fuses, connections ect