Remember, he's not teaching you how the DAW works in that course, he's just teaching you music theory.
His examples are in Logic, so he's using Logic's Scissor Tool to divide notes and Logic's Glue Tool to combine two shorter notes (of the same pitch) into one longer note. Those tools are NOT available in GarageBand. In GB you can divide a note by selecting it, positioning the playback cursor where you want to cut the note, and hitting Command-T. Sometimes Command-J seems to work to join two shorter notes (of the same pitch) into one longer note, but most of the time Command-J DOESN'T work, so if you have two shorter notes (of the same pitch) you'd have to manually Trim the edge of one of the notes (and delete the other one) to make one longer note.