I need to build a process that creates an email alert that uses a template but first needs to prompt the user for some information such as date and time, etc. Is there a way to do this via Process Builder/Flow? Limitation w/Flow is that I cannot use email templates with it, therefore I need to create an email alert, and the problem with Process Builder is that I cannot use screens in my linked Flows.
The Process Builder is strictly for running on object insert/update like workflows. In your case, you probably want to use Flow, save the input values to your record, and then use workflow to fire off the email alert based on those values being set.