I have had some of the problems you noted previously. But here is what I ended up having to do.
First, when connecting the Apple Airport Extreme Base Station (AEBS), I first took the Airport Extreme Software Disk and loaded that on my PC.
Then, because it did not see my AEBS, I ended up getting an update to the Airport Utility by an ethernet connection.
Then, I had to reset (hard reset) the AEBS and re-do all the settings. I ended up doing all that several times and finally got everything working.
Then, apparently when I uploaded Airport Utility 5.3.2, none of my PC nor my MACs could see the Airport Extreme -- and -- I just did not want to reset the AEBS all over again.
So, I called Airport Support and they asked (since I was connected to the Internet via wireless -- though the Airport Utility could not "see" the AEBS) me to connect via Ethernet directly to the AEBS.
By doing so, my AEBS was immediately visible via Airport Utility (and without doing any hard resets of any kind).
Then, I changed the channels under Manual Setup to one that was not being interfered with by neighbors -- and as soon as I did that, all my MACs and PCs (well my MACs for sure) and I also assume my PCs because now I can print directly to a printer connected via wire to a wirelessly connected PC to the wireless network -- that I could not do before.
Now all the while I used a CLOSED network for security purposes.
Hope this helps someone out.
It seems that the reason the Airport Extreme Base Station is NOT visible via Airport Utility (including 5.3.2 -- which is the one being used) -- the problem was solved.
All this was done by a very knowledgeable support member at Apple Airport support.