Several years ago I installed SUSE 11.3 and I added several package with YAST using the graphical user interface. At that time it was all "singing and dancing", everything worked fine.

The only part of this installation I now would like to "modernize" is Firefox! But it is not working!

• I start YAST
• I select "Software"/"Software Management"
• I search "firefox" and get a list of "Packages" with a "hook" for "MozillaFirefox","MozillaFirefox-branding-openSUSE","MozillaFirefox-theme-oxygen"
• I check "dependencies" and finds that the installed version is "3.6.6-1.2" and that the alternate version is "3.6.24-0.2.1". Looks like that the alternate version is an old version too!

But clicking "Accept" results in absolutely nothing!

• Is the problem that "Software Repositories" is set to 11.3? Should I use a newer Repository?
• Is it perhaps not possible to get a newer version of Firefox without starting everything new with the complete latest SUSE release? Am I otherwise stuck to release 11.3 for everything, also for Firefox

No such thing as "SUSE 11.3". Do you mean

1] openSUSE 11.3?

2] SUSE Linux Enterprise Desktop 11 Service Pack 3?

Either way what you're using has long been unsupported and you need to do some major upgrading.

Still it should be possible to download only FIREFOX with dependencies fitting the SUSE-LINUX setup without touching the rest of the system! The installation of a new Firefox version into an existing (older!) MS Windows system is standard! Is it possibly OK to just replace the old binary "/usr/bin/firefox" without touching any other elements?

That's not really how Linux distros work.

Linux is not Microsoft Windows.

If you do it right, it might work, yes. You can download Firefox direct from Mozilla, unpack it and see if it runs.
https://www.mozilla.org/en-GB/firefox/new/
If it does, you can replace /usr/bin/firefox with a symlink to the new Firefox binary. But you're really just trying to polish a turd by doing that. You're using a version of Linux that is hopelessly out of date and unsupported by it's vendor. It's like still being using Windows XP. You should upgrade your entire Linux installation and you'll get the latest Firefox as a part of that. Whether your best course of action is to do an in place upgrade to the latest version or do a clean install will depend in part of what you've done to the current install (any third party repos added?) and what you mean by "SUSE 11.3" (see my previous post). If it's openSUSE 11.3 re-install is your best bet as there's seven releases between that and the current version. SUSE Linux Enterprise 11 Service Pack 4 is a current supported version though.

on the long unsupported opensuse 11.3

11.3 went END OF LIFE in Jan 2012
there is NO new firefox

now you MIGHT??? be able to run the firefox from the mozilla web site ???
MAYBE???

but DO NOT expect firefox 51 to run on a 5 year out of date OS

11.3 is EOL
11.4 is EOL
12.1 is EOL
12.2 is EOL
12.3 is EOL
13.1 is EOL
13.2 is EOL

the current is OpenSUSE leap 42.2 ( renaming and merge with SUSE ENTERPRISE )

I have at present time a laptop and a desktop both running Windows XP. Both with the current version of Firefox. In addition a desktop running Windows 7. I consider it a myth that XP needs to be replaced with Windows 7 - 10! The reason for this myth is that Microsoft wants to continue its business!

Then I als have 2 other desktops both running openSUSE 11.3. They fullfill all requrements! Used as WEB server, FTP server, for program development!

But OK, I now install the current openSUSE on a 6th computer! If this should be my new standard Linux computer fullfilling all the tasks of the previous ones I will have to do at lot of installations! And all this stupid fuss just because of Firefox!!

NO ,it is NOT !

11.3 went END OF LIFE!!!!! back in 2012 !!!!
there have been NO UPDATES ,NO NEW SOFTWARE, AND NO SECURITY FIXES!!!!

Warning:
-- !!! DO NOT USE !! --

If you are still using Windows XP on computers, especially if they are connected to the Internet, you are putting yourself and your data at risk that would be easily mitigated by upgrading your OS.

If you are running using openSUSE 11.3 to host a web server exposed to the Internet then you fail to meet the basic competency required for such a responsibility. I hope that you are not being paid to run it.

Neither Windows XP nor openSUSE 11.3 are supported by their vendors. That means there are no updates. That means when vulnerabilities are found that affect versions of software/libraries/whatever in those operating systems, there will not be any updates to fix them. openSUSE 11.3 went End Of Life in January 2012. That means it is vulnerable to every exploit discovered in the last four years. The bash Shellshock bug was disclosed in 2014, which potentially allows an attacker to execute arbitrary code on a system running a web server. ImageTragick was disclosed last year, which again potentially allows an attacker to execute arbitrary code on a vulnerable system. Those vulnerabilities alone could be sufficient to turn your web server in to part of a bot not or host malicious content. Combine them with a privilege escalation vulnerability, which I know there's been at least one of in the Linux kernel in the last four years though details currently escape me and I'm too lazy to fine them, and the attacker has root.

Keeping your operating system up to date is not "stupid fuss", it a fundamental concept of computing security.

openSUSE 42.2 is the current release of the freely downloadable version of SUSE, and it's a good release, plus you can readily obtain MozillaFirefox (Firefox) updates - I know it has 50.0.1 for certain, and if there are any really recent released updstes, it either has them or will have them within a matter of days, since it's currently supported.

In the past week, I ran and updated this distribution, and while I cannot recall from memory which Firefox update it provided, whatever it was, it appeared to be the same current update that I have on my other distributions and it was easy to install and maintain, so I recommend it.