Hmm, no mention of which Linux distro. Thus it is hard to give definitive answers since each distro is different.
1) I always prefer to download the bin file from the Sun
Java download site and run it (whether you download the *rpm.bin or *.bin depends on your distro). Others use the package manager to install it (some distros do not offer this option).
2) Download the ZIP file from the JBoss AS download site and unzip it somewhere. By the way, there is no AS 4.3.0.GA, the only 4.3.0 designation is for EAP which is a commercial ($$$) product. The latest 4.x release is 4.2.3.GA. But you really should be using 5.1.0.GA.
For more detailed steps see:
http://community.jboss.org/message/203487#203487
Also, JBoss in Action provides detailed installation steps (they are pretty much the same for 4.2.3 and 5.x)
3) Use the package manager to install it.
4) See the JBoss Cache documentation (further discussion on this topic should be done in the JBoss forum:
https://coderanch.com/forums/f-63/JBoss)
5) Not sure of the context of this question. Are you asking how to add logging to the app you are writing? Or how to configure JBoss AS logging? Or how to configure Linux logging with regards to JBoss AS? Or something else entirely?