IPad – What options to mirroring iPad display to Windows 10 PC that balance cost and performance

You might like to checkout Writepad - it sounds like it does pretty much everything you are asking. I've used it before, and found it worked pretty well. It's only $4.99US at the moment as well, so maybe a good time to give it a go.

I also use Plecodict which is an English-Chinese dictionary, which has handwriting recognition for learning new characters (and an optical recognition mode as well) - just mentioning it because you didn't specify a certain language.

Good luck.

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.