How many days for this tour??

If you haven't booked flights, it's always best to book MULTI CITY tickets -- fly into one city and out of another to avoid having to circle back to Frankfurt. Like fly into Frankfurt and out of Munich. Saves lots of time and typically isn't more expensive. Will you have a car, or just be using the train?

2 weeks minimum; preferably 3.

The answer is How long do you want to spend in each town? Plus travel days. That's for you to decide. Count nights, not days. My choice would be minimum two or three nights each which is 1 to 1/2 or 2 to 2 1/2 days per. Maybe more if you like the town. Travel time and checking out of and into hotels takes up time. How many people are "we"?

I'm going to Munich for the first time in June and spending 5 nights total there (first stop, last stop), plus cities in Austria and a RS tour.
I hear that hotels are booking fast so you need to decide soon.

As part of a longer trip, I have a week planned for just three of the places you mentioned, so as CJean stated, a minimum of two to three weeks would be needed. I don’t feel multi-city tickets are the best way to go, however, they certainly are an option. It depends on your itinerary.

What is it you want to see/do at each location? How long will that take? Add for travel time between each destination, and you have your answer.

If you spend 2 nights at each place ( to give you one whole day, plus some fractional part on you arrival/departure days) takes 3 weeks.