SWFPut provides a video players for posts and pages and widget areas, as both flash and HTML5 video.
Post a comment at http://agalena.nfshost.com/b1/?page_id=46 or email edhynan at gmail, or of course go the the SWFPut WordPress page at https://wordpress.org/support/plugin/swfput and select the "Support" tab.
Probably not. In most case the width and height of the video will match the intended display proportion. "Anamorphic" video is not rare, but probably not too common either. The author has seen videos on e.g., YouTube, that are distorted by wrong display aspect ratio (which is not YouTube's fault), but only a few. If you find that your video looks squeezed or stretched, you can always use a little trial & error with the display aspect setting until it looks good.
What you must understand is that you must convert video to the format (the type) that the plugin or browser can handle; namely, FLV or MP4 for flash; and, MP4 and OGG and WEBM for HTML5 video. Web searches will yield plenty of resources on video file formats, but many of them will be difficult to understand if you are not experienced with digital video and its formats.
If you use a converter program designed for non-experts, you won't need to understand too many details. A web search should turn up some converter programs that might be worth a try.
Update: now it does. In the words of Emily Litella, "Never mind."