Unfortunately not, when you use a threshold and email, you can't get ALL of the messages, only data from one of them, and if you have a big OR, it's kind of hard to guess what to send - you might have to use a somewhat generic template .
If you use an Event Group you might be able to accomplish something similar and get more data into the email (an Event Group is kind of like a built in OR on Event type), but it will still just be one of the events.
In either case you can use that "Rule Fired" or "Sent Email" event to search in LEM and then click through the Event Explorer to see the history of all of them, though. It's not quite as clean, but the data is there.
not out of the box, but you can do this using a SQL query in your alert email message.
search for that and LMK if you don't find anything useful and I'll try to help.
I have to agree with Nicole and Njoylif.
What I have done for other clients is to dump the relevant info in a text file (which is reachable by http), then the final email will point the user to the link.