The video should be in mp4 (with H.264 encoding).
You can place the video in InDesign using File > Place.
You can scale the video before placing it in InDesign (e.g., using the Adobe Media Encoder), or simply scale the frame within InDesign.
There's no "correct" video size, but here's what screencast.com recommends:
iPhone and Android Recommendations
You can use the iOS Simulator (along with MAMP) to test on the iPad and iPhone.
To test from the web, you can use Chrome or Safari and open the local file. Firefox works better with MAMP since it uses the Flash Player to playback the video and there are security restrictions on the local machine.