Maybe this website:

• https://www.apkmirror.com/apk/mozilla/

I was hoping it would pop up the file-downloading dialogue when I click "download" button on mozilla.org.Not google play , or any other apk sites.

In this thread: https://support.mozilla.org/en-US/questions/1269114

Link: https://www.mozilla.org/en-US/firefox/all/#product-android-release

those are for android 4.1 ++ but not for Android v 2.3 gingerbread

The Android Firefox has required Android 4.1 at minimum for a good while now.

Firefox 48.0 for Android required Android 4.0 at minimum then https://www.mozilla.org/firefox/android/48.0/system-requirements/

As of Firefox 56.0 for Android the minimum was raised to Android 4.1 https://www.mozilla.org/en-US/firefox/android/56.0/system-requirements/

If you are really determined to still use that old vulnerable device and vulnerable versions of web browsers then you could try to side load Firefox 47.0 for Android as it supposedly still support Android 2.3

http://archive.mozilla.org/pub/mobile/releases/47.0/ and pick the one for your cpu.

https://support.mozilla.org/en-US/kb/will-firefox-work-my-mobile-device

The Android Firefox has required Android 4.1 at minimum for a good while now.

was hoping it would pop up the file-downloading dialogue when I click "download" button on mozilla.org.Not google play , or any other apk sites.