Your iOS is way out of date, Skype probably won't run on it, upgrade your iTunes to the latest version then upgrade your iPad and hopefully it will all be resolved.
No problem, there are a gazillion of us using iPad 1 on the latest version of iOS, many apps are designed only to run on iOS 4.xx, you have nothing to lose and everything to gain.
If you look on the app store Skype for iPad will only run on iOS 4.0 and beyond so if you want it you have to upgrade. You do need to bear in mind that you will be able to receive video feeds via Skype but you can't send video.