Authorizing iTunes on an iPad

Correct. You do not have to authorize the iPad. You do want to be signed into the same iTunes account with the same Apple ID that you use on the computer with your iTunes library. After you authorize the computer to download iTunes content and you sign into your account on the iPad - you are good to go!

Not in that same sense. For the most part, you can use any number of iDevices, that all have the same Apple ID and iTunes account of them as you care to use - for personal use. There is no limit. If you have 20 iDevices, and you use the same ID on all of them, that is fine.

That 5 devices limit is strictly for computers with one iTunes account.

I have my laptop and my Ipad on the same Itune account and it works well. I have been trying to download some of my stuff on the my children mini ipads using my name/password but it said I need to wait 90 days? Does it mean I can only have one ipad on my Itune ? I wanted my children to be able to see some of the movies I bought. Did I miss something ?

You must have used another ID on the kids iPad minis and downloaded previously purchased content with that other ID. When you switch ID's on an iDevice - and then download a past purchase with that ID - you have to wait 90 days before you can switch ID's again. You can only associate a device with an Apple ID once very 90 days.

This is to prevent users from switching from one ID, to another ID to another ID, etc, so that they can download content again without having to pay for it.