And what program is responsible for these dialog boxes? Is this part
of a Windows or Firefox security feature?
It's part of neither. If you'd done us the favour of translating the error messages it would have been easier and I wouldn't have had to resort to an online translator. Anyway, the last word on the dialog very clearly mentions which program is responsible, i.e. JRE.
Should I be concerned about a possible infection now? Or was the infection diverted?
For the benefit of others, this is what the message translates to in English:
Presumably the applet was indeed blocked as stated and no malicious code got executed on your system. Even if code did get executed perhaps there's a chance it wasn't able to break out of the Java VM's sandbox and affect your system. Of course, given Java's poor security track record there's no guarantee an exploit hasn't compromised your system despite those messages.
I'd suggest: i) thoroughly scanning your system with multiple anti-malware tools, and ii) disabling Java if you don't use it or at the very least update. What are you doing running an insecure/expired JRE anyway?
For extra credit you may want to read the Setting the Security Level of the Java Client article, which states the reason for the dialog:
Ensuring the Most Secure JRE
Before the browser plugin software attempts to run a Java app, it
verifies that the JRE version is at or above the security baseline for
that family and that the age of the JRE is recent. If the JRE is
deemed expired or insecure, additional security warnings are
displayed. In most of these dialogs, the user has the option to block
running the app, to continue running the app, or to go to java.com to
download the latest release.
JRE Expiration Date
The JRE relies on periodic checks with an Oracle Server to determine
if it (the JRE) is still considered up-to-date with all the available
security fixes (above the security baseline). In the past, if the JRE
was unable to contact the Oracle Server, it continued to behave as
though it is still the most recent version with regard to security for
an indefinite period.
To avoid this problem, a secondary mechanism, which does not rely on
external communication, has been added to the JDK 7u10 release. From
this release onwards all JREs will contain a hard-coded expiration
date. The expiration date is calculated to end after the scheduled
release of the next Critical Patch Update.
This means that JREs that are unable to contact Oracle Servers for an
extended period of time, will now start offering additional protection
after a reasonable period and will not continue to behave as if they
were still up-to-date with security fixes.