Will Mozilla firefox conflict at all with my Macbook Pro operating system?

Question

Will Mozilla Firefox conflict with my Mountain Lion operating system and Safari?

Answer 1

No, why should it?
Any program you install can contact the Internet, if you don't like the Safari web browser (and many don't) then your certainly free to install a alternative.
Just don't install a web browser from AppStore, because Apple has a 4-8 week delay while they review all apps there, leaving a window of opportunity for your machine to be hacked.
Security Issues Warning List
Harden your Mac against malware attacks
Apple is notoriously slow in issuing security updates for OS X, Safari, iTunes etc, doing so many months (or in one case 3 years) after being notified of the issue.
https://krebsonsecurity.com/2011/11/apple-took-3-years-to-fix-finfisher-trojan-h ole/
To install Firefox you'll likely have to head to Apple Menu > System Preferences > Security > General and where it says Downloads select "Anywhere" (you can always turn it back later)
Then visit this page, check the status of your plugins and there also is a download for Firefox on the same page.
https://www.mozilla.org/en-US/plugincheck/
It will be in your Downloads folder and you open that, double click the installer or package to open it to show the program and drag it to your Applications folder, then from there drag a icon (alias) to the Dock so you can access it quickly.
Firefox has tons of Add-ons, more than anyone else.
https://addons.mozilla.org/en-US/firefox/
Plus tons of persona's that dress up the browser
https://www.getpersonas.com/en-US/gallery/All/Movers/100
It's a customizable browser, there are already many themes others made
https://addons.mozilla.org/en-US/firefox/complete-themes/
It also auto updates by itself and the add-ons, security issues are fixed very rapidly and can come out within hours of a exploit being known.
So it gets updated very fast, unlike Safari which is glacial.