When support for XP SP3 stops in October 2018 will Fire Fox still work?
I realize that there will not be updates after that date so I will have to rely on my own malware and antivirus, but will Fire Fox still function?
Opaite Mbohovái (2)
Yes, just like Windows XP still starts up and runs, Firefox 52.9.0esr should still start up and run even after its last update.
Security. Over time, more vulnerabilities in the old code base will be discovered by bad actors. Security software can help protect you from some of those. Avoiding tempting links and blocking bad sites also is important. For example: https://www.opendns.com/home-internet-security/. Ultimately, there's no substitute for software that is patched up regularly.
Functionality. Over time as websites move to newer technologies, Firefox will have more and more problems browsing, but hopefully by then you'll find a replacement for your entire system so you can have software that is getting regular updates.
Moambuepyre
The legacy Firefox 52 ESR will be EOL on Sept 5th with no more planned for updates after.
Firefox 53.0 and later requires Windows 7, 8 (8.1), 10 to run.
Firefox 52 ESR was made for Enterprise users in mind as it was a bonus in being a option for Windows XP and Vista users to still have a version with security updates for a while longer.
Firefox 52.9.0esr will still work however with no more security updates and using it on the vulnerable EOL Windows XP is risky. You really should be using Windows 7, 8 (8.1), 10 or switch to or dual boot with a light Linux distro like Lubuntu or Xubuntu among other light options that still support 32-bit CPU.