Mailer error log? Not sure what you mean by that.
Your email even if it is sent can fail seconds, minutes, hours, days later.
Depending on the sophistication of your CPanel email settings for your mail boxes, it is possible to set up filters to deal with bounced and undelivered emails.
As for your other question...
You will always need the Reply-to value set.
In your server create a no-reply@ email address and set that mail box to expire / delete any incoming emails. It is handy to set a default reply message stating that the person has responded to a no reply email address and that they need to go to the website contact point or give an email address they can email.