My Azureus is working fine with the latest Spybot program and current updates.
Admittedly I have stuck with the older Azureus release - Azureus v3.0.5.2
I am not using the newer Vuze Client v3.1.1.0 as I just want the classic features.
You appear to be reporting two problems:
The TCP port you have configured inside Azureus appears to be blocked.
A website is unavailable to you -
http://www.azureuswiki.com
My first response as a tech support and user of both programs would be:
Spybot doesn't block TCP ports - so not sure how it could be responsible.
I doubt Teatimer is responsible - but why not try turning it off as a test.
The current Spybot Immunization package is not blocking the website you mention.
Have you actually run the NAT/Firewall test option in Azureus or are you just seeing the warning indicator? The fact that the Azureus program reports you are firewalled just means it can't see any inbound connections - which can just be that there are no current peers wanting to share. However if the NAT/Firewall test also fails then the TCP port you have configured is being blocked by something - either on your PC or in your Router. If you really have no software firewall active then most likely something has changed on your Router.
The fact that one website is not available for a period may just be co-incidence - is it still down for you? Did you try to access it direct or via the link inside the program?
What about any of the other Azureus related websites:
http://www.vuze.com
http://sourceforge.net/projects/azureus/
How about this direct link to the wiki NAT/Firewall problems page:
http://www.azureuswiki.com/index.php/NAT_problem