hack or something similar on my iPad Air
Go to Settings > General > Profiles and Device Management. Delete any profiles you don't remember installing, then restart your iPad.

Next, update it to the latest version of iOS (9.3.2), this should remove the Jailbreak, if there is one, as that version cannot be Jailbroken.

As for what caused it to send spam to your contacts:
If the iPad had malware, well, obviously that was it.
If not, did you sign into it on any other devices?

Also, does your daughter use an iPhone, iPad, or Mac? If so, you can use FaceTime instead of Skype.