Firefox for Android is installed via Google Play and you need to update Firefox via Google Play, so updating should happen automatically if you start Google Play regularly. You can also check the current state in Android App management and the history in Google Play.

About your Firefox version on Windows 7:

Firefox 116 requires Windows 10 as the minimum and users on Windows 7 and 8 and 8.1 have been moved to Firefox 115 ESR.

• https://support.mozilla.org/en-US/kb/firefox-users-windows-7-8-and-81-moving-extended-support
• https://download-installer.cdn.mozilla.net/pub/firefox/releases/115.7.0esr/

While browsing a site

What site?

Try disabling your extensions.

Firefox on Windows works extremely well. On my cell phone (Samsung A32) it also works very good but I cannot find anything in the Settings or Help (again on the cell phone) to check for updates? I immediate went to find a "Check for updates" button in either Settings or Help. I could not find anything. Could someone suggest how to check on my Android cell phone (Samsung A32) if the Firefox is up to date?

https://support.mozilla.org/en-US/kb/update-latest-version-firefox-android

Since you are asking about Firefox for Android, I moved this thread from (desktop) Firefox section to Firefox for Android section.