I know you cannot use a single P-trap, except for a kitchen double sink.  If you have 2 bathroom sinks, they would each have thier own trap. 
 
As for your vent, there is usually 1 or maybe 2 common vents in a house.  All fixtures have to be vented properly.  If you are adding something that is not close to the common vent get a licenced plumber to do it. 
 
The AB code does require the permit for plumbing to be pulled by a licenced plumber.  Electrcial you can pull & do yourself. 
		
	
		
		
		
		
		
	
		
		
	
	
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