If you're willing to pay for an app, Exchange by Touchdown will do all that. It has a 30 day free trial and then the key is currently on sale for $9.99.
It is working well with my company's Exchange 2003 server. It will only synchronize your local contacts, not the global address book, but local contacts sync great, as does the calendar. There is a TouchDown for Tablet from the company also listed, but it doesn't have support for the Fire for some reason. It also includes a remote wipe option including an email initiated one. It will only support one Exchange account at a time however (have to switch profiles).
For company email, I'm a fan. Now if I could only find a GMail client I like. (And yes, I've tried all the ones mentioned here, what I'm missing most is threaded messages.) (I like to keep my personal and company inboxes separate.)