It sounds like you are having difficulties getting FaceTime activation to work on your iPad min. That is certainly a frustrating situation.
I would suggest following the steps in this article to troubleshoot this issue -
If you see "Could not sign in, please check your network connection and try again" when signing in to your Apple ID
To resolve this issue, follow these steps.
- Update to the latest version of iOS.
- Verify that you have a data connection by going to www.apple.com in Safari. You can complete Apple ID activation using Wi-Fi or a cellular data connection. If you need help connecting to Wi-Fi, follow these steps.
- If you're using Wi-Fi, make sure that your local Wi-Fi network is using the recommended Wi-Fi settings.
- Sign in to your account and ensure that the primary email address and alternate e-mail addresses have been verified. If verification is pending, follow the instructions in the email Apple sent to that email address to complete verification. Or remove the e-mail addresses from the account.
- If your Apple ID isn't an email address, you can change it. The Apple ID that you're using to activate FaceTime or iMessage must be an email address. Find more information on how to change your Apple ID.
- Tap Settings > General > Date & Time. Make sure that your iPhone is set to the correct time zone. If Set Automatically is on but the wrong time zone appears, turn Set Automatically off and choose the correct time zone, date, and time.
- Enable iMessage and FaceTime while connected to a different Wi-Fi network (in a different location) if a cellular data connection is not available.
You can see that you've activated FaceTime and iMessage with your Apple ID by following these steps.
- Tap Settings > FaceTime > You can be reached by FaceTime at:
- Tap Settings > Messages > Send & Receive > You can be reached by iMessage at:
Thanks for using Apple Support Communities.
Unable to make or receive FaceTime calls after April 16, 2014
Using FaceTime http://support.apple.com/kb/ht4319
Troubleshooting FaceTime http://support.apple.com/kb/TS3367
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To send messages to non-Apple devices, check out the TextFree app https://itunes.apple.com/us/app/text-free-textfree-sms-real/id399355755?mt=8
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Apps for Texting http://appadvice.com/appguides/show/apps-for-texting
You can check the status of the FaceTime/iMessage servers at this link.