IOS – What’s the best way to remotely access an iPad mini

I think you are going to need an iTunes account, but you can get around the need of a credit card. You can follow Apple's support documentation on how to setup an iTunes account without a credit card. You can use a Mac to make a free account that works on iOS and iOS to make a free account that works on Mac. Once your iTunes store account is set up once, you might want to avoid creating a second one since they cannot be merged later.

• Creating an iTunes Store, App Store, iBookstore, and Mac App Store account without a credit card - https://support.apple.com/en-us/HT204034

1) Yes, if you join the paid Apple developer program, you can install apps on your own devices without going through the app store. You won't need to release an app to be able to use it. (It's also possible to run self-signed apps on a jailbroken device without joining the program, but that's kind of a pain.)

2) You can cache web applications locally, but there is some extra work involved in doing that. However, it's probably not as steep a learning curve as learning Objective-C. Here's a little information about developing these apps, from the excellent Dive Into HTML5. Local web apps won't be as fast as native apps, and you won't have access to hardware features, like the camera. You can't even upload photos from Safari (which local web apps always run under).

3) Yes, you can add video to presentations in the iPad keynote app. If you go this route, you might also want to get an app that allows you to fill out and sign contracts on the device. There are several of these, but I don't have any experience with them, so I can't make any recommendations.