The "From" address is what the form submitter enters in the "email" field.
The sender is usually the same value. But, for various reasons, your server has been honest about the sender being the user "nobody" on your server.
Some spam filter somewhere has probably decided that this mismatch is unacceptable and is rejecting the mail (without telling you!! and this is why I think spam filters are a really bad idea! We don't use spam filters and we don't get much spam - but that's another story.)
So, there are a number of ways to attack this problem. First, make sure you have version 5.02 or later of FormMail.
Next, read the documentation above these FormMail configuration settings:
And also read the release notes for version 4.03 (this describes the FromAddr feature).
Get your alerts working first. If they are not working, then you're making things hard for yourself.
Use the testalert feature:If you don't receive alerts then you need to set $FROM_USER to a valid user on your server. You may also need to set SENDMAIL_F_OPTION (but I don't think so because your server seems to be using Exim instead of Sendmail).
Once you have alerts working, try your form submissions. If they still are not working, then you'll need to use the FromAddr feature in your HTML form to set the sender and From address to a user on your server.