To answer your questions:
1. They would immediately play .mp4 (and possibly .mkv files.. I'd suggest MPEG4/h.264 video encoding)
2. I think .mp4 is a bit more widely accepted container (it shows more media info in Windows Explorer as well)
3. No, they just treat them as any other downloadable file, like a .zip file for example.
4. Only after you download the whole movie and play it locally (in a few minutes, when the download completes).
In reality, it is not just the download speed and size/volume of the video file that matters, the compression/encoding algorithm is what makes a huge difference. MPEG-4/H.264 video and and either AAC, AC3 or MP3 audio currently produce the best picture/audio qualities per Megabyte, they are very efficient and are widely accepted/adopted by most browsers/Operating Systems/mobile devices. H.265 is the next generation encoding, but I don't think it has caught on yet to be worth worrying about.
MKV, MP4 and WMV are just "container", or "wrapper" formats. What it means is that they can contain a MPEG-4/h.264 video stream in them already, or, other types of video/audio streams. The difference is that MP4 and MKV are widely accepted by most devices and Operating Systems, including Android, PlayStations, mobile devices, etc., while WMV is Microsoft proprietary container that no longer plays on many modern browsers, even the add-ons for Chrome no longer seem to work.
Here are some tools that can help:
Handbrake (converts to .mp4/mkv, it is a great free tool):
https://handbrake.fr/
Fast conversion from most formats to mkv:
https://mkvtoolnix.download/
Microsoft Windows Movie Maker (Free):
https://support.microsoft.com/en-us/hel ... r-download
Conversion to MP4 (havent used this one):
http://www.videohelp.com/software/MkvToMp4
GSpot (it can identify the video/audio codecs in the current wmv container format, if you are interested):
http://www.headbands.com/gspot/v26x/index.htm
I hope I haven't caused more confusion, I do realize how time-consuming re-encoding can be. I like using Handbrake, one can add multiple input video files and just let it run.