I submitted the first 10 pictures, but were rejected because "Maximum size for illustrations is 25 megapixels. Can I submit the same pictures again, but the right size? Is this really was the only reason for rejection?

Normally, you'll have to put a note to the reviewers writing why you are resubmitting.

But being the first 10, I guess you can just resubmit after correcting the issue. Rename files after downsampling, just to be sure they don't reject based on automatic check.

Is it the only reason? No way to tell since they only state one reason. But while you're waiting to resubmit, you may post your pictures on the shutterstock critique forum, here:
http://submit.shutterstock.com/forum/viewforum.php?f=4

yes you can resubmit . . .
good luck

Thanks for the help!