/usr/lib/jvm/java-1.5.0-gcj-4.4
This is not a qualified JVM to use with JBoss AS. The 1.6 version you mention for question B, is that a Sun JDK that you downloaded? If so, change JAVA_HOME to reference it. You will also have to check the soft links for /usr/bin/java (and other java-related soft links) to verify that they all point to a Sun JDK,
I suspect that most likely when you ran JBoss AS from the command prompt that you somehow got the 1.6 version, but Eclipse is using the gcj-1.5 version.
By the way, the answer you gave for question A is not what I asked for. I asked for the full name of the file you downloaded. I asked that because the full name gives a hint as to whether the binary you downloaded is for JDK 5 or 6. I still do not know what you have since you did not specify the name of the file you downloaded.