Could try this
https://obsproject.com/
It's fairly popular as a powerful livestreaming tool for streamers on sites like Twitch.tv (I think) but you can definitely use it for recording your screen as well.
As for editing, not sure about free options.
Conversion: I don't think it's possible to convert replay files but I might be wrong. I'm fairly sure people like Roger does it by screen recording their replay as it's being played on client, which actually isn't really a conversion.
Edited phrasing a little.