How you save a transition depends on how you've created it. You can create a transition, for instance, using the Gradient Wipe, or you can create a transition using two video tracks and one of the transition Presets (like Blur In/Out).
But if you're asking if you can save a transition based on your customization of a transition's properties, the answer is no. Sorry, you can't.
As for sound effects, there are many sites out there, and you can find lots of effects just be doing a Google search.
Chuck Engels also has posted links to a couple of great sound effects and music sites on his web site.
And, of course, you can find many of them right inside SmartSounds Quicktracks, which is included with Premiere Elements 7.
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Here are some URL's for SFX. Some are free, and some for pay:
One final question - what file format would it be best to download for sound effects?
WAVs are the best format for audio files. MP3s are the best second choice.
If I am given the choice, WAV will be my #1. Unfortunately, most are in MP3 format, which is highly compressed. However, I have never had an issue with the MP3 SFX files. That is the only time that I do use MP3, as I will convert all music, and such, to PCM/WAV before Import into Pr. Still, with hundreds, or maybe thousands, of MP3 SFX files, I have never had one issue. I just like to get as close to the "source," as I can.