For H.264, look under the iPod group, IIRC. There you should see the H.264 MP4 and other options, like variations on MOV.
Flash will be just that - FLV.
Are you saying that under MPEG option the H264 choises are unavailable? Please clarify.
There are a number of ways to export MP4s from a Premiere Elements project.
As Bill says, you can export it for portable devices using Share/Portable Devices/iPod.
If you're exporting it for display on the web, you should use John Cloudman's output settings in the FAQs to the right of this forum. (Although you are selecting the MOV output, it will come out as an MP4 because you are using the H.264 codec.)
Thanks, as I had forgotten to give the full path with "Portable Devices."
Yes, any format that uses the H.264 codec will produce an MP4.