Premiere Elements can have trouble identifying the specifications of MOV files. Most likely the program is not automatically setting up the program to match the video's specs. (This would be indicated by yellow lines along the top of your timeline in Expert view.)
What model of camcorder is your video coming from and what resolution and codec does your video use?
Did you use Premiere Elements' Add Media tools to get the video from your camcorder to your computer?
If you don't know, you can open a sample of your video in Media Info. Once we know your video's resolution, frame rate and, above all, the audio and video codec it uses, we can give you some specific solutions.
SG should be in a better position to reply to your MacBook Air Premiere Elements 12 question than I since he has worked with Mac computers and Premiere Elements. I am strictly an Elements Windows user who "reads" about Premiere Elements Mac.
But, certain aspects of your question caught my curiorsity....isn't that 1.3GHz clock speed for the dual-core Intel Core i5 on the low side?
I did a quick Google Search, and it would appear that there is a Turbo Boost up to 2.6 GHz mentioned with that product. Have you used that and gotten any better Premiere Elements performance?
You're definitely right, ATR. MacBook Air's are built for portability, not power. They're great for surfing the internet and doing basic Office work -- but they're really not built for powerful computer work, like video editing. (MacBook Pro Airs are a different story.)
Turboboost will probably not make appreciable difference -- at least with version 10 -- but hopefully we can help the poster optimize his workflow and see what happens.