Safari of my Macbook (on WiFi) suddenly fails to connect to the Internet. A popup window message says another device on the network is using my computer's IP address.

Question

But then there was still no Internet access even after I have disconnected all other home computers (a total of four including the Macbook and one iMac desktop.  For simplicity, I shall categorically called them Mac hereafter unless otherwise specified.  The Macs are operating on WiFi.). 
The window message recommends changing the IP of either the Macs or the other device.  The latter of course does not apply because I don't think the other device is one of my computers. 
My questions:  
(1) Why did that happen suddenly since the Mac and other computers on the WiFi was working fine in the morning (as well as days before) and then all of a sudden an unknown device is using my computer's IP?  As far as I (we) can remember, we did not do any thing unusual this morning nor had we downloaded any special programs.
(2) How do I change the IP since it requires Internet acess to do it and since I can't access the Internet on the Mac? 
(3) I am almost sure the problem is not caused by the Internet service because when I connected the Ethernet cable from the DSL modem to an old Windows PC, I got Internet via Internet Explorer.  [I am actually sending out this message via IE on my PC.]  However, when I cennected the Ethernet line from the modem to a WiFi router (Airport Extreme) and then connect the router and the old PC, I did not get Internet on either the Mac nor the PC.  Similarly, there was no Internet on both Mac and PC If I connect Ethernet only between the modem and the router but not between PC and router.  So, the question is whether a third unknown party has gotten hold of my Mac IP address and is trying to break into the Mac?  Can it steal my personal info?
(4)  How can I repair the Mac now and prevent future recurrences?  Is changing the IP address the way to do it?  (But like I said before I had tried but could not change the IP because I did not have Internet access on the Mac.  Is there an alternative method?) 
(5) I wonder if a computer's IP address remains constant if you don't change it.  The reason I am asking this question is because the aforesaid window message on the Macbook--not sure about the iMac--shows a different IP address--a few numerical digits were changed--almost every time it pops up following every failure trial of mine to access the Internet.  Was the Macbook trying to change the IP for me or was there some thing not right?

Answer 1

Re: Another device on the network is using your computer's IP address.
This message/problem was occuring intermittently for me in a household with two MacBooks accessing one Airport extreme.  Rebooting the modem and router would only temporarily fix the issue for me, so I spoke with a friend who works for Apple and it seems that the Airport Extreme settings were at the root of our particular issue.
The router(Airport Extreme) recieves only one IP address from the modem and in order to allow it to share the IP address with two computers at once, the solution in my case was through:
Applications>Utilities>Airport Utility>Manual Setup>Internet
under Internet Connection- Select "share a public IP address"
under NAT, check the box for "enable NAT Port Mapping Protocol"
   (this will allow the sharing of one public IP address with multiple devices)
if this is a new setting, then click "Update" and the Airport Extreme should reboot itself with new settings applied.
When all else is working properly, this is a satisfactory solution in my case.