The transfer time is 7 minutes at Freilassing but I see it is from Platform 2 to Platform 1,
so there shouldn't be a problem time wise, correct?
Correct. But as always, be at the door of the train car before it stops, and get off when it does and find the stairs to the tunnel (Gleis 1 and 2 will be on different platforms). Since most people getting on the Berchtesgaden train will be changing from other trains, they will probably hold the Berchtesgaden train if the train from Munich is a little late. If not, oh well, there will be another train to Berchtesgaden in an hour, at 11:40. The later train still gets you to Berchtesgaden at 12:28, giving you enough time to catch the Eagles Nest tour.
A Bayern-Ticket is easy to buy from a ticket automat at the station. There will be one or more at Rosenheimer Platz S-Bahn station or at Munich East (Ost). You can buy it ahead of time; just make sure you put in the correct date as once purchased, it is non-refundable and non-exchangeable and only valid for that date. You also need to fill in the names of those traveling on the ticket before boarding the first train.
To save time at the station, you could purchase it online from the Bahn website. Make sure you put in four passengers, then put in from Muenchen Ost to Berchtesgaden, the date you'll want the ticket for and the time. Actually, the to: and from: and the time don't matter (as long as it is after 9 AM on a workday), and the website offers you the Bayern-Ticket for 4 people (@43€). Regardless of the actual train(s) selected, the ticket will be valid for any regional trains in Bavaria all day long.