Download the ActMailing tags plugin for JEvents here.
To include your latest events in your newsletter simply insert the tag {jevents} to show all the events that match the plugin parameters. If you want to restrict these by category you can do so like this {jevents|catids=12,15,35} - this would show the events that are from category 12, 15 and 35.
Download the JMail Alert plugin for JEvents here.
[jev_latestevents] in your alert template to show your latest events at that position of your alert.