you can use the bpm plug-in o find out the bpm of the song.
Remixing is a big topic... it all depends on what you are trying to do, the style, do you want to use the whoel song and just add to it, or take elements from th song and use in a remix...?
Firstly, remixing a whole song without the individual tracks is gonna be very tough in general.
However, you can cut out some elements from the song (vocal lines, drum hits, etc) that are relatively alone in the song (not crowded by other instruments etc)...
...make a drum beat you like, on a different track add the cut our regions from the song and start cutting and pasting around to try out an arrangement...
Is that helpful? I'm not sure as it's difficult to advise without knowing the style you are going for and the original material.
Do listen to your favourite artist's remixes to understand how it sounds, and how much of a track they may remix.
If you don't already have it, Logic 101: Core Logic 8
Will be helpful to understand more about how to add synths and create drum beats, as will the ES2 exposed and Ultrabeat and the Logic 404 Mixing with Olav Basoski may inspire you too:
Do check out the preview videos first to see what would suit you & of course feel free to ask us any more questions.