How to stop Time Warner cable search on Firefox for Android? I went into about:config and have the following:

browser.search.defaultenginename
Google

browser.search.official
true

browser.search.order.1
Google

keyword.URL
https://www.google.com/search?p=


And still, when I type in the search bar, it pulls up Time Warner Cable Road Runner search instead of Google. It looks like only if I have more than 1 word does it decide to use google -- maybe using only 1 word means I type a malformed URL? How can I fix this to use Google as a proper search engine?
Your issue is not related to Firefox but to your internet provider (Time Warner Cable). According to this site, it "hijacks" your browser's default DNS resolution failure behavior (also known as "404 page"), redirecting you to Road Runner.

Following this site instructions, you just have to go to Road Runner's preference page and disable the Web Address Error Redirect Service option then save.