Click on the Vimium icon in your Chrome's toolbar. From there you can permanently exclude the current site. Or, if you prefer to mix Vimium's shortcuts with the page's own shortcuts, then you can add a more sophisticated set of exclusion rules.

You can also view and edit all of the sites for which Vimium has been disabled on the options page.

Visit chrome:https://extensions, and tick the box Allow access to file URLs next to Vimium.

(Some users have reported that you need to untick then retick this flag when Vimium upgrades.)
(The box Allow access to file URLs moved to extension Details)

Chrome disables all extensions on these pages, for security reasons. There's no way for Vimium or any extension to run on those pages.

Vimium's basic functionality requires that the Vimium javascript be loaded into every page. Vimium requires access to bookmarks and history because it has a UI which replaces Chrome's URL bar (called the "Vomnibar bar") which autocompletes queries with suggestions from bookmarks and history. Vimium never talks to any servers and does absolutely nothing with the data. Also see the privacy policy.

Unfortunately this isn't supported by Chrome's extension API. However, Vimium has its own implementation of the Omnibox (called the Vomnibar) which is chock-full of hotkey goodness. Hit o to access it. Note though that the Omnibox can be accessed via Chrome's default shortcuts to focus on the Omnibox (namely Ctrl-l and Alt-d).

The Omnibox is the URL box in Chrome. It's super handy, but you can't access it using Vimium's shortcuts. This is due to a limitation in Chrome's extension API. We can't script Chrome's omnibox in any way. In fact, we can't even focus/unfocus it programmatically.

As a workaround, Vimium has a lightweight replacement for Chrome's Omnibox. It's easy to focus using a single keyboard shortcut, and it has a powerful and very practical completion system. You can also use it to help you jump to any tab or bookmark.

No -- unfortunately extensions cannot access the custom search engines which have been configured in the browser.

However, there's a workaround: here are instructions for quickly setting up custom search engines in Vimium's Vomnibar.

This is because chrome doesn't allow extensions to run on tabs which are in "view source" mode.

The New-Tab Page now supports Chrome extensions. Chrome focuses the omnibox when the New-Tab Page is opened, so to use a Vimium command you should focus the page by clicking, double-tapping <F6> or pressing <Tab>. If this isn't to your liking, you could try using an extension which bounces the new-tab page to a page of your choice which supports Vimium better.

Chrome won't let extensions like Vimium interfere with certain application-level key bindings.