You may need to set Android to allow installation of apps from other sites. This might be under your Android settings in Security. (Although you should actively get that option when initiating a download.) You could also check settings in Chrome for anything meant to keep your device "safe".

Also make sure you are on a stable wifi connection, as that can be an issue.

You may also wish to reinstall Chrome to make sure it is not broken, or so out of date that the SSL certs are bad.

P.S., this is obviously not a firefox issue. You may get much more help in an Android site forum, particularly places where they promote options other than google.

Samsung apps you should be able to update from Samsung without a browser, although the do have some of them in google play these days

One last thing to make sure - have you checked your Downloads folder (or wherever you chose to save the files)? In most cases outside of googleplay, apps will not automatically install - they only download.

Another option, of course, is to download on a computer, connect your phone, and sideload apps that way.

You can download the latest Firefox for Android APK at https://www.mozilla.org/firefox/android/all/