Regarding question #1, AVI and MP4 are different video formats, paul is correct that they are containers but a 720p movie in AVI is NOT necessarily the same quality as an MP4 (it is almost always less quality) and if it is the same quality it is almost always going to be a much larger file. The reason for this is video codecs use different amounts of storage to store a video, the older and less efficient codecs require MUCH more space for the same quality. For example MPEG 2 (the codec DVDs use) requires up to 4 times more space for roughly the same video quality that MPEG 4 (what Blu Ray uses) offers.
A note about resolution, 720P / 1080P do NOT refer to quality but rather the resolution of the video, the compression rate and the codec used affect quality of videos of the same resolution. A 1080P file streamed on Netflix / Amazon / Itunes (~ 5 mbit/s) is MUCH lower quality than a Blu Ray disc (30 to 40 mbit/s).
Nearly all consumer phones / tablets and digital camcorders use H264 or another MPEG 4 variant today. You can use a free program called Handbrake (http://www.handbrake.fr
) to convert AVI files to Mpeg 4 (which is usually actually using H264).