I want Tor Browser to use my real IP address when I use my Google account and my Facebook account so as to skip the security question. I want to use Tor Browser as my default browser because Mozilla crashed too much. I don't need to hide my IP.
Welcome to Tor SE, I'll try to answer your questions, but I also have some comments.
Although it is possible, you should never attempt to use tor browser without tor. Switching back and forth between your hacked not-anonymous tor browser and the not-hacked tor browser would be a personal burden on you that you will eventually make a mistake doing that. If you want to remain anonymous, only use tor browser with tor. If you want to use your real ip address, don't use tor browser.
Assuming by "Mozilla" you mean "Firefox" (made by Mozilla), I would take a step back and look at your situation. If firefox is crashing so often that you are getting annoyed by it, then you have probably done something very wrong. I would look into why your firefox is crashing. Is it a virus? Have you installed a buggy extension? Is your firefox severely outdated? An up to date firefox should not be crashing at all.
As for accessing google and facebook. Once you establish a track record of using these services through tor, they will stop questioning you about why you are connecting from a weird ip address. If by security questions, you are referring to having to solve captchas (or similar), then this is unavoidable through tor at the moment, as this is how most services allow you to prove that you are a human.
Final note: it's tor, not TOR. Although tor was originally nothing more than "The Onion Router", it has since evolved into an entire anonymity ecosystem, and the change in nomenclature to tor is to break the idea that tor is nothing more than a router.
Like the above, there's no point in using the Tor Browser Bundle if you don't want to use Tor. It's slow and cumbersome if you don't need the features.
You can try using Firefox ESR 31.6.0, which is what Tor Browser 4.5a5 is based on. It should be functionally equivalent, aside from the ability to browse hidden services and connect via Tor not being present. You can install NoScript as an addon if you still want to disable scripts in Firefox ESR.
If you want to keep the ability to use Tor but want to avoid some hassle with Facebook, in October 2014 Facebook launched a hidden service. I believe accessing Facebook over the Tor hidden service reduces the hassles involved, but I may be mistaken. Either way, it lets you take advantage of the enhanced security offered by Tor Browser. The service can be accessed at https://facebookcorewwwi.onion/. Google has yet to implement a Tor hidden service, so you're out of luck there.