Is it possible to change the sender e-mail in the e-mail alerts setting?

I would like to change the sender e-mail from "noreply@jotform.com" to my business' e-mail address; is this at all possible? 

Hi,

Yes, that is possible. Check this guide: How-to-Add-a-Custom-Sender-Address-to-an-Email-Alert.

You can also try using Mandrills SMTP: How-to-use-Mandrill-to-Send-Emails-From-Your-Own-Email-Address

Please contact us again if you have any questions.

Have a great day!