I couldn't really find an answer by searching, so I figure it's okay to ask: does the 2000 C280 use a timing belt or chain?

 

The C280 uses a duplex timing chain,as do all modern Mercedes engines from the early 90's. Before that they used a single row chain , as far as I know MB have never used timing belts.
Geo.

 

how can you tell when they are getting bad?

 

If the car is serviced regularly the timing chain on your car should last at least 200k miles, so unless there is a problem I wouldn't worry about it.

 

Shouldn't it go for the life of the engine?

 

If well looked after these engine can run for well over 250k mls but the chains do wear and because of the stretch the valve timing alters reducing the efficiency of the engine ,so I would say for this reason alone 200k is a max before changing the chain.
To answer your question , if the chain breaks it is usually uneconomic to repair the engine, so that's it's life .