The belt and pump prices seem ok. Anything around 400 for both is about right.
If your flywheel is clattering you can usually diagnose it, to some degree, by dipping your clutch when you're sat in neutral. If you dip the clutch and it's silent, but then get lots of noise when you release it, this might point to an issue. However, flywheels can be a bit noisy but not actually be faulty. It's the nature of what they are. I assume the mechanic is quoting the total cost for flywheel, clutch and labour - it makes a lot of sense to do clutches and flywheels together. From what you've described though, about the noise going away, I'd suggest investigating other causes.
The engine lurch - this is a common thing. A popular theory is that it's caused by carbon build up. A failing injector can also cause a rough idle, like a series of small misfires.
I think the best thing you can do right now is get a second opinion. Where are you based? Unfortunately, anyone can call themselves a 'specialist' without actually being one. And the big thing, you're not confident in these guys. That seems obvious. You don't have to hand over your hard-earned to anyone you don't fully trust.
So, have a search around the forum, see if you can draw up a little list of recommended specialists near you, and go from there.