How do we change the exim configuration and do we rebuild?

[skurudo]

first, do we edit /etc/exim4/exim4.conf.template when we need to change something?

Yep, enable/disable spam/virus check for example, change dkim selector, change relay IP or something like that.
Exim conf file have many options. When we make changes, need to restart exim service.

second, after we edit that template do we have to "rebuild mail" for that user?

This is for user, correct.