The 500 had 512 chip ram and 512 fast ram.
Unfortunately, you failed to notice TS was talking about an A500+ (plus), which, like the A600, has 1 MB chip mem as standard. Through the trap door, it can be expanded to 2 MB chip mem max, just like the A600.
Apart from that, the standard A500 (without the '+') only has 512 KB chip mem and no fast ram at all. Through the trap door, it can be expanded to 512 KB chip and 512 KB fast (well...) mem ór to 1 MB chip mem.
There's not much technological difference (if any) between an A600 and an A500+, apart from the pcmcia and on board ide-ports.
Amigas really need both chip and fast mem.
No, it does not. Any Amiga runs perfectly well without fast ram, although extra fast ram makes it a nicer experience. And yes, there are programs which need fast ram, but for most programs it is just optional. Highly recommended to have some fast ram (4 MB will do nicely in most cases), though.