I was actually just helping our data team with this the other day..
- First Launches: Don't find any event/field related with that
There are two options, the first is to use mobilelaunchnumber and you would have to look for "1" as the value to find the first launch. However, the actual event is passed as part of the event_list and you will need to use the events.tsv file to map the value correctly, I believe this is "700" also called "mobileinstalls" in the events mapping reference.
- Single Page Visits: Should I apply any logic in the data through the visit_num and visit_page_num?
I believe this you have to calculate yourself and yes, using the fields that you specified.
- Orders: I assumed that the Event is Purchase (1) so in the event_list field should appear 1 (LIKE '%1%')
Again, similar to First Launches (or any event), all events are passed in the events_list field, and you need to map the correct numerical value using the mapping file. I believe orders is called "Purchase" as you surmised, but you can't just use a SQL query to look for "Like '%1%'" or you will pull out every event number that contains a 1, and since that would include Cart Open (10), Checkout (11), Cart Add (12), Cart Remove (13), Cart View (14), every single "instance of eVar" which all start with 1, every custom event that contains a 1, etc....
You would be getting super inflated counts with that SQL. I believe that events come through in order, so you may have to look for Equals '1' OR Like '1,%' (basically look for exactly "1", or starts with "1,"