First, I think your .AVI's are going to need a special codec that you may not have. Can you open them in QUicktime? They may not playback, but they will tell you the codec if you choose WINDOW/SHOW MOVIE INSPECTOR or hit COmmand-I. Under format it should tell you the compressor used.
Avi's aren't great for Mac's in general because they tend to use strange codecs that are hard to get. My bet is it is using some proprietary codec from Premiere or something.
As for the .yuv, that file extension I've never heard of, but it could be telling you that it is in the YUV colorspace like Christophr mentioned. When you change it to .mov or .avi and try to open with Quicktime, what does it say? Does it give you an error or does it open, but just doesn't show video? If it opens then hit the command-I again and give us the specs on the codec, listed under FORMAT.
Do you know what kind of camera this video was shot on? Do you know what/where the original files came from, what system? Once you can determine that we could probably help more.
I did find this link that might help:
www.fileinfo.net/extension/yuv
It is saying to use the Mplayer to viw the files. The fact is, that you'll need to get Quicktime to recognize them, so if that requires loading Mplayer then do it. Then, drop them all in Compressor and switch them all over to a ProRes 422 file. Then you'll have an easier time editing them.