Vim style Omnicomplete for emacs?

Answer 1

There are a number, all a little different:

• predictivemode
• pabbrev
• completionui
• autocomplete

They all have their drawbacks and advantages.

The emacs wiki has a page for all the completion packages.

Answer 2

I think company mode would best fit your description. Have a look at it.

Answer 3

Can you? Sure. Reset a timer on post-command-hook. If it goes off (because you are sitting at your screen not typing), pop-up the thing.

It seems easier to tell your computer what to do (by pressing keys) rather than having it wait for your to stop typing for a while, however. Bind completion to something like the "menu key", and you won't even have to chord.