Is it possible to install Google Chrome web browser on an iOS device?
You can now install Google Chrome on an iOS Device.
Do note that it does not use the Chrome Rendering engine, but uses the Safari webkit. The "killer feature" though is that it has syncing with your Google Account.
No. It's not possible to run Chrome in iOS.
I don't see why you'll want to run Chrome, even if it exists.
Safari for iPhone uses WebKit, the same rendering engine that Chrome uses. There shouldn't be much difference between the two. Safari is plenty fast on the iPhone.
The only other browser available for iPhone is Opera.
It is not and I doubt that there will ever be such a port, because the model Chrome is based on is that each tab is run as a separate process. As there is no true multitasking in the iPhone (available in public APIs, that is) such app would not be possible to do.
If Google ever releases something like that (which would not be approved in the App Store, with the current rules, but for argument's sake let's say it's released as an ad-hoc distribution, or as source code) it would work very differently, thus being a different product with the same brand