Can I manage the template/text of email which the users are getting at the time creation of users, creation of courses, assign users to courses or will I have to change in the core files to change the contents of the mails?
yes, you can change that (and much much more) under language management. This means you can also have different content in different languages.
look for e-mail module or look for the text you want to change
Do not edit what you might find under [....].