1) The entire file is not downloaded.
2) You will be able to check when the file is requested via the Network panel to see if the start requests are being set.
3) Just make sure to encode using HandBrake, use the default settings and web optimized. - http://handbrake.fr/, alternatively, if you have an MP4 already and just need to move the meta data, this tool can be used - http://renaun.com/blog/2010/06/qtindexswapper-2/
Finally, you need to make sure that you actually install the mp4 pseudo streaming module for your web server, and in your JW Player embed code, set a startparam value, which is either start, startime, or apstart, depending on your web server configuration. We have a guide about this here - http://support.jwplayer.com/customer/portal/articles/1430518-pseudo-streaming-in-flash
Keep in mind, if you are using html5 , the pseudo streaming module is not needed, as html5 already does this, and the pseudo streaming module is really only for Flash.