Welcome to Android Central! Chrome is the main browser, although some devices also include a stripped down stock Browser, sometimes also called Internet. I would imagine the G2 only has Chrome preinstalled as a browser. You can try out other browsers on Google Play, including Boat, Dolphin, Maxthon, Opera, and many others.
The Google app you're referring to is probably the Google search bar. When you search using the search bar, the results are displayed by Google Search, but if you click on a link, it'll open up in Chrome.
You can set up your default Email app to import mail from Hotmail, but you can also do that with Gmail. If you go to your Gmail account on your computer, there are settings where you can import other mail like Hotmail. Then, you could just rely on the Gmail app to read all of your email.
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