You should confirm that the Contact that receives the email (To Specific Contact on the Step record) has a valid email address on their Contact record. If you dynamically identify the Contact through the Email To Contact field, confirm that all potential Contacts have valid email addresses. If the email address is empty on any Contact who is supposed to be emailed, the email sends to Default Contact instead.

If you don't know which template you're using, go to Administration > Processes, and open the Process. On the Steps tab, open the Email step, find the Email Template, and click the jump link next to the template name. You'll go to the Template's Message record, where you can click Edit and make your changes.

If you know which template you're using, go to Communications > Messages, and open the message. Then, click Edit and make your changes.

Yes. The On Submit field can contain SQL text that executes when a Process receives a record submission. The system uses the text in this field in the "SET" clause of an UPDATE statement.