Lots of questions... I can only answer a few of them, but maybe enough to help you.
Firstly... those hard-wired desktops... if you have a single IP address from your provider, you must be using NAT to get the WiFi clients working. Whatever is providing the NAT service for WiFi clients can also provide it for your desktops.
Why have you got a mix of Linksys and D-Link WiFi gear? Deploying mixed hardware is more likely to lead to confusion and increased support problems later on.
Anyway...
You say that the wireless signal is weak on each floor. That may be due to the construction of your building and/or the position of the WiFi equipment. Usually WiFi equipment is mounted in a high position - frequently on the wall - to ensure obstructions to the signal are minimised.
To build a building-wide WiFi network properly you need signal plotting tools (not cheap) and time to experiment.
Without these tools, you're down to experimentation by roving around the building to see where the weak spots are, reposition the access points and rove around the building again to see if it's better/the same/worse.
You also appear to suggest that the access points are running on Channel 11. Is that right? Are all of them on Ch.11? If so, they will interfere with one another and degrade the signal strength - that alone might be the main cause of your problem.
Despite the number of selectable channels in WiFi networking, in fact, they overlap one another and this causes interference. Normally, channels 1, 6 and 11 are used as there is less overlap between these. Use a different channel for each WiFi access point.
You have four access points but only three clear channels to play with. You will need to experiment to see what works for your location but you may find that you can use Ch.1 on the top and bottom floors without too much interference. If that doesn't work out, try channels 1, 5, 9 and 13 (if that's available to you).
I can't answer your questions on the config settings for your Linksys kit.
I would strongly encourage you to troubleshoot your network from the basics. Switch everything off and start with your primary connection to your provider. Make sure that is working, then move on and add only one device. When you are fully satisfied that device is working, add the next device. Only make one change at a time, otherwise you won't know what change caused the problem. Your Linksys access points should have the same configuration, with the exception of the channel.
Good luck!
