Don’t cut it close since 40% of long distance trains are late. Everybody has horror stories but you can usually get where you’re going if you pay close attention to the electric departure boards in the stations! The lines are often long but the information kiosks can be very useful and they almost always speak English.
Train passes can be good, but you have to pay close attention to all the rules and whether they fit your plans. Some passes allow travel within a calendar month while others start the clock ticking when you board the first train. It’s tricky, so be careful. Furthermore, if you do well with the agents, theater auditions can come up at any time. You may do better with a BahnCard. They give you 25 or 50% off the full fare. I always favored the 50% (the 100% is only for commuters). Again, find out the current rules online or in a Reise Zentrum at the train station, but some of them have a three month trial period and you can get some money back. Be sure to cancel, however, and again, check the exact rules. The DB also has cheap advance sale tickets, but once booked they can’t be changed or returned.
I used to hate overnighting for an audition but it’s probably a good strategy these days, especially for young singers. Prices are high and flights may be cheaper but you have to get to and from the airport so check those out too. If the trains were dependable you can get most anywhere in Germany within 6 or 7 hours, but now that may not be the case. I used to enjoy going to gigs and auditions on the train: it’s relaxing, you’re isolated and can study. Getting food and drink at the station was interesting and fun, if a bit expensive, and stretching and walking around is ok. I even vocalized in the bathrooms (WC)! Not ideal, but sometimes necessary!