My Rsx started making a rattling sound under the car out of the blue, I took it in to the dealer and they adjusted the valves and replaced a motor mount, and they ordered a part for my exhaust to have put in, charged me $1300 for the fix. After a week of driving it, out the blue the Rsx started and then just shut off, and now won't stay on. I took it back to the dealer and now they're saying it's my timing belt and my valves are broken and it'll cost me 2k to fix now. The car only has 113k miles on it. Is this common? Is there something fishy going on with the dealer?

Timing belt failure (breaking or slipping) on these cars is catastrophic, because they have interference engines. Timing belts should be changed every 90,000 miles or 7 years, whichever comes first. That's not a bad price. Ensure they replace the water pump at the same time.