Assuming they are Drum brakes most likely the wheel cylinder is bad.
It could bend valves.
yes
Front disc, rear drum
Depends on your driving habits.
The brakes :)
Rear wheel yes, four wheel was an option.
you go to a mechanic, because this is probably the best advice you will get on the web.
Haynes repair manual, Dodge Neon 2000 thru 2003. Book #30036
anyone in there right mind would not to remove breaks on a car. Really!!
check your calipers,theymay have froze up
sounds like an exhaust leak, or a fuel leak. that depends on the smell.
Replace brake lines or wheel cylinder which ever is leaking