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The trip from Orvieto to Cortona is very easy. There are two stations you can use to access Cortona, Camucia-Cortona and Terntola-Cortona. Of the two, Camucia is a bit closer and there are frequent trains on that route with a travel time of about an hour each way, some direct and some with one change. I'd suggest the direct trains, which are currently at €7.50 PP each way (DON'T forget to validate your ticket prior to boarding the train on the day of travel, or the cost will rise sharply when you have to pay a hefty fine!).
When you arrive at Camucia, you can use either a Bus or Taxi to get up to the town. I can't remember where to buy Bus tickets but a nearby Tabachi is the first place to look. It's about a 15 minute trip on the Bus as I recall. You'll be dropped at the Bus station in Piazza Garibaldi (which is nothing more than a sign), and it's a short walk from there to Piazza della Repubblica (where the Andre Rieu concert was filmed).
For the trip back to the station, there's a Tabachi just downhill from Piazza Garibaldi. Buy a Bus ticket there and you're all set.
I'd have to give some thought to your second question, so don't have any suggestions at this time.