Reading the Manual will clarify some things.
FCP and almost every other editing application doesn't like compressed video and audio, which you have provided with .mp4 and .mp3 files.
I don't know the settings of the source files, like resolution and frame rate, but use MPEG Streamclip to transcode the video to .mov files using the DV (SD material), Apple Intermediate Codec (AIC - HD video) or ProRes (HD video) codec.
And transcode the audio either to .aiff or .wav.
Then import again, and set the SEQUENCE SETTINGS similar to the video and audio.
And again, read the manual, it provides a helluva of information about this, you have just spent a grand on that piece of software.
If you still have problems, please post the specific settings you used for the sequence and what format and codec and resolution the video and audio use.
Also MRoogle will find you plenty of threads about "using videos from the www in Final Cut Pro".
Even though some might get annoyed of reading this, the thread title guy strikes again:
A more descriptive and precise thread title will help cater to the right audience and get you more responses.
To edit your thread title, just click on the
button on the bottom right of your original post and then click the "Go Advanced" button below your message.
Have you also taken a look at http://mroogle.*************/MRoogleSmall.gif, since that question may have been asked several times?