I am building a web app…and this will have a support and contact mail so the users can communicate with me for technical problems or for requesting simple info.
Do you think that these mails(their content)sent by the users of the app should be stored in a database table?
What happens to the mail is your choice. It may just get mailed to your inbox and nothing more, or you can keep a permanent record in a database if you like, or both.
On form-mail scripts I have made, I do both, send an email to the selected recipients, but also keep a record in the database. This has helped on occasions where the mail has failed to send (unreliable php mail() function). If I check the DB, I may find mail that I had missed, and have an archive of mail recieved.