you can create a self-signed certificate using animate and see if that will allow you to install on your ipad. i really can't remember if that will work, but i think not.
to be sure, whoever's publishing needs a certificate from apple to install on ad hoc ios devices.
android certificates can be self-signed even when uploading to amazon/google.
For #3, yes, you can make your own Android certificate, post an APK online somewhere, and anyone with an Android device can install the app, without it going to Amazon or Google Play. The user will have to go into their settings to enable side loading of apps.
For number #2, if you had the $99 developer account you could then add up to 100 devices to your account, and all of those devices would be able to install the app. It will expire though, in I think 6 months. You would have to republish the app and have the client install again.
If you want a permanent install without the app store your client would need an enterprise account, and would need to give you access to their account so that you could make the certificate you would need. Or someone working for the client would need to send you the certificate to use. I don't think that you as an individual would qualify to get an enterprise account.
For #1, read this article on how you can get a certificate for free, that you would be able to install apps onto your own devices. It won't help with the distribution to the client's devices, but at least you could develop the app without paying $99. The article talks about LiveCode, but the steps should still work for Adobe AIR:
Thanks for the detailed answers!