A few things you need to know:
An "MP4" file can have a million different kinds of settings.
Frame rate, size, data rate, etc.
Whatever your Sony shoots as a "native" file, it clearly isn't playing nicely with FCP7.
The solution:
Transcode it.
That means, you need to use software like Apple's "Compressor"(which you likely already have installed), Quicktime,(GUARANTEED this is already installed) Handbreak, FFMPEG, or (IMHO) the one that beats them all and is free : MPEG STREAMCLIP.
If your camera is shooting in HD, I would recommend transcoding it to "Pro Res."
This seems to be the codec of choice at the moment.
It's going to take a while, be warned, so if you have a secondary computer to do the transcoding while you work on other stuff, this is advised.
Another thing you can try, is plug the camera via Firewire to you Mac, and choose the menu in FCP called : File/Log and Transfer.
This will automatically transfer the footage from your camera to your hard drive.
Cheers
Treatment