Re: Changing an audio files tempo...
Well, I forget with Logic 7 - but time machine should work fine. However, you may need to make sure you convert the audio files from mp3 to aiff again as Logic doesn't play well with compressed audio formats.
So try to bounce the files to aiff and then re-import these versions into Logic.
As far as making a dj style set - this isn't Logic's forte. If you want to change time and pitch in realtime (on the fly) then I'd recommend looking into something like Traktion of Ableton Live.
Logic 8 has basically the same pitch and time correction as Logic 7, including the ability to create your own Apple Loops and then use the tempo global track to time stretch regions. Logic 9 has flex time and varispeed which could add something new and useful to your setup... but still Live may be better for your needs.