I do not know much (yet) about mastering, but I would suggest the following:
1. Import the single audio track from your handheld recorder to your computer.
2. Import the track into logic; you should be able to just drag the icon from the desktop onto the track and it will copy and show up as a blue audio region.
3. Go through the single track and cut it up into pieces, dividing each song. To do this, move the playhead to where you need a division and click the icon "split by playhead" at the top. This cuts the region wherever the playhead is.
4. Now that the single long audio track is divided into sections, create some new tracks (Command-Option-N). You can now drag each segment from the long track to the new tracks until you have separate tracks for every song.
5. I would recommend exporting each song in one of two ways; either right-click the region and select "export as audio file" or you can click the solo "S" button in the lower right, click on one of the regions, which will highlight yellow, and click "Bounce" at the top to do essentially the same thing.
6. When you open the exported audio file outside of logic, it will copy to itunes. From here, you can name the files, arrange them in a playlist and prepare to burn.
I hope this helps!