Hi, I doubt he could get your IP off of skype, and even if he did, there is not much he can do with your IP. Plus you are behind a router, so you don't have much to worry about. Plus, unless you have a static IP, you probably already got a brand new IP, just by turning your Wifi off, and then back on again.
Just install some antivirus software, and you shouldn't have anything to worry about. Microsoft Security Essentials is free, and very good.
Make sure your Wifi has proper security. You should set it to use WPA2 Encryption if available, and choose a complex password.
If you have done all of these steps, you should be good to go. If you are feeling paranoid, change the password of your WiFi, and run a virus scan.
About the IP conflict: make sure your DHCP server is turned on in your router (it should be on by default) Make sure the IP of your laptop is set to automatic (again it should be automatic by default) Also make sure that all of the other devices accessing your WiFi, or network, are all set to automatic, or if using staic IP, choose some IP that none of the other devices are using. If you need any more info, just write me.