At the moment there is no standard widget for showing (youtube) video's.
You can show a static video on your start page (see this question). But that question only deals with video's on your start page! Video's on a start page is possible by adding a youtube HTML tag in your theme package (startpage.mxf). But editing other .mxf files is absolute no option, they will be overwritten when deploying your project.
In short: you need a custom widget for showing the video's.
Note: Uploading and downloading video's is no problem, use the file manager widget for that.
You can use a video (e.g. youtube). As far as I know, uploading a video directly in your Mendix application is not possible yet. Again, you can use a site like youtube to upload your video. If you have placed your movie in your application then you can use your theme package and the html to show this video in your desired form. Note: you need a custom widget to accomplish this functionality.
I would also like to refer to this question and answer(s).
Is it also possible to make some sort of report functionality which shows if the logged-in user actually started the movie and viewed it all the way through?