1. I can't figure out how to have an effect only occur during a few seconds of a clip (like if the clip was 30 seconds and I only needed the effect for 5) without splitting the clip. Is there an easy way to do this?
This is accomplished using keyframes. For a basic understanding of keyframes, visit the VASST website. Keyframing is used by every NLE out there, so you'll need to learn how to use it at some point.

2. How can I get two clips to show up at the same time (splitscreen)?
Use Pan/Crop or Track Motion to move the clips to the locations you want them visible. Track motion is usually best for this, but not necessarily.

3. How to do slow motion?
Grasp the edge of the clip, hold down CTRL, and drag to desired length. Or right click and change the playback rate. Or right click and insert a Velocity Envelope and set the speed there.

4. Is there any way to show only a certain section of a clip (a box around what you want to show with the rest blacked out)?
Use Generated Media templates, found in the View>Media Generators tab to locate what you want, drag it to the track above the clip you want to black the edges of.