RE: [1] They show the exact same page for me both on Firefox and Chrome when I search for GOOG. I use Firefox as my main browser, and am logged in to my Google account on Chrome.
This has been such a noticeable problem that a Firefox add-on (Google Search Fixer) was created to fix it:
https://addons.mozilla.org/en-US/firefox/addon/google-search...
Google Search Fixer is currently available on Firefox Nightly for Android.