You bring up an interesting topic. I would ask your ISP if you are allowed 2 IP addresses at once. Is your usual IP from your ISP static? Mine are not, I get a different IP from my provider pretty often. Most endusers can change their IP if they like, but there are some exceptions to that. I am not sure exactly what happened with you and your ISP in having 2 IPs at once, but it could be an error somewhere on their end with the router.
Did you check with your ISP to see if you are allowed 2 IPs? I know I am not entitled to that. I look at IP addresses all the time and I check my own often to see what it is.
If you want to check an IP to see if it blacklisted, try a metasearch that compiles a bunch of different RBLs (real time blacklists) (including Spamhaus) at http://www.robtex.com/
then go to the blacklist tab or use http://www.blacklistalert.org/
if robtex is down. Sometimes these blacklist checkers have spotty web performance. Some of the blacklists are extreme, but if you see CBL blacklisting your IP, then I would be concerned about a compromise. With the other listings, it varies tremendously, as they could be blocking a very big IP range and not just yours. You can change the last octet of your IP to check and if it is blocking a range of IPs, then someone else on your IP range is the culprit.
When I first checked out the second address, there was an ad from a broadband company about securing my address designation. That company was legitimate according to my other applications and a check on WHOIS, but why was it highjacking a tab?
That I am not sure. I would definitely scan my system to make sure it is clean.
I had heard a few months ago that the internet would run out of addresses in a few years. Well, it hasn't been that long. And why do I have to share my address?
Supposedly, IPs (on the current IPv4) are running out in a few years. I have been hearing about it for at least a decade now. But keep in mind not all IPs are being actively used right now, not by a long shot. Most large swaths of IPs are allocated and way back before the Internet got very popular and commercialized some entities like universities and older companies like IBM received huge numbers of IP addresses. Certainly they do not use all of them. For serveral years now ARIN ( American Registry for Internet Numbers) the organization that allocates IP addresses in the US) is very strict on handing out the remaining IP ranges to organizations online. They check to make sure existing IPs are used properly (this is due to the anticipated shortage) So while we supposedly run out, the next generation protocol IPv6 will be implemented across the Internet (and it will be expensive to do this) and that will allow many more IPs to be used.