At the very least we need to know exactly what software you are using if we’re gonna be able to help.
If you are using the Sansa software then yes there is a chance that you don’t have enough free space, but it should be telling you. Once it’s done converting it, it will copy it to the player, but if it can’t for some reason it should tell you that.
It is slow because your computer is slow, or you have too many applications open for it to run fast, or not enough RAM, or any of a huge number of reasons but probably just because you think it’s slow. A 4 minute video from youtube takes me about a minute on my 2GHz core2duo and is around 15MB. All of the video converting software is equal in speed, more or less. This speed is more than acceptable for anyone that doesn’t work for a movie studio 
Search this forum for “FuzeVidz” for a nice drag-and-drop converter. I like it. It’s converter backend is one of the best out there.
