How I can save the Skype chat history from my iPad?
It would be nice if Skype (Microsoft) synched the message history from your iDevices to your Mac where it is easily accessible, but I suspect they don't.

In the meanwhile you can try a trial version of something like iExplorer (https://www.macroplant.com/iexplorer/) which can access most/all files created on iDevices and try to locate your Skype message history.