This is a Firefox support forum, not a mac one, so we won't be able to help with the specifics of updating your mac, but Apple has a good support page set-up at http://www.apple.com/osx/how-to-upgrade/ to help you get from 10.7 to 10.11.
Mac OS X 10.4 can be installed on an iMac G5 by inserting the Mac OS X 10.4 installation disc into the iMac and double clicking on the Install icon. Microsoft Office for Mac 2008 may be the best pick for business users, with major updates to Word, Excel, PowerPoint, and Entourage. Paid Microsoft Mac OS X 10.4/10.5/10.6/10.7 Version 12.3.6.
Microsoft Office For Mac Support
Microsoft Office For Mac
As for iOS (and you should be running the most recent version of iOS for security reasons) both Firefox and safari are equally secure, as they both use the same backend (Apple won't allow a competing backend on ios), but if you are using Firefox on your computer, using Firefox on your iOS device will allow you to sync your bookmarks and other data between devices (Sync your Firefox bookmarks, open tabs and browsing history in iOS)