For the forced download you need to send out the file headers first.
header('content-type: application/zip');
header('content-disposition: inline; filename=YOUR_ZIP_FILE_NAME_HERE.ZIP"');
For zipping you'll wanna use one PHP's zip libraries, then echo/output the zipped content.
http://ca3.php.net/manual/en/zip.examples.php
Something like this:
$zip = new ZipArchive();
//the string "file1" is the name we're assigning the file in the archive
$zip->addFile(file_get_contents($filepath1), 'file1'); //file 1 that you want compressed
$zip->addFile(file_get_contents($filepath2), 'file2'); //file 2 that you want compressed
$zip->addFile(file_get_contents($filepath3), 'file3'); //file 3 that you want compressed
echo $zip->file(); //this sends the compressed archive to the output buffer instead of writing it to a file.