some of the video experts familiar with premier may help more than me but a couple suggestions.
video files are always huge, especially if you're shooting with an HD camera. I think you need to edit at the native resolution, but you can downsize when you export the edited movie. I don't know premier, but you usually choose Export from the File or another menu and can choose the type of file and compression ratio to suit your needs. You may need to experiment with different ones.
With the transitions it could be a couple things, if you haven't rendered the sequence yet, it my flicker because the program can't handle the transition b/w large files. The most likely cause is if you don't give enough extra space at the end of the clip.
If, for example, you have a 30 frame transition, there must be at least 15 frames BEYOND the MARKED end point of each clip to allow the transition. If you mark the end point at the actual end of the clip, there's no room. Or, if the shot changes (i.e. when filming you stopped & restarted recording) within 15 frames of the MARKED end of the clip, you'll see that shot change inside the transition, creating a flicker. Just navigate through the transition frame by frame, using the arrow key, to see exactly what happens.
This can be really irritating and when starting you quickly learn to always give a couple seconds of extra room at the beginning and end of each shot when filming just for this purpose.
Hope this helps. Cheers,
Chris