Can I receive e-mail alerts, or something similar, from noticeable events?
Like, when someone fails to login at the router web page or some client gets disconnected.
Yes but you’d have to use the custom JFFS scripts to read the logs and email you. 15 mins work if you are comfortable with scripting, many hours/days of head scratching if not!
Might be easier to install your own syslog server (potentially on the router under entware) that will have an easy option to generate an email based on certain log events. Just a matter of adding the syslog IP info to the General Log, Remote Log Server to have the router direct it’s logging at it.