Which Railway Pass to Buy and Travel Tips

Please don't take offence, but most of your planning is completly unrealistic. Please have a look on a map to locate Lauda, which is in the middle of nowhere. The only maior town that is in reach within one hour is Würzburg. On April 13, having a whole day, you might be able to visit both Würzburg and Rothenburg; everything else is illusionary, esp. since you can leave Lauda daily after 5pm only. I'd concentrate on the delightful minor towns in the region, which include Wertheim, Miltenberg, Tauberbischofsheim, Bad Mergentheim, Wertheim, Creglingen and others (a car would be helpful for some of them).

This is always the wrong first question. Instead of 'which pass', ask yourself whether any rail pass is needed. Frequently the answer is 'no'. You can only decide by working out the cost of point-to-point trips on your own, then comparing the total to what a pass costs. Remember, as well, that on trains requiring reservations the passholder has to make a separate reservation purchase, at extra cost. For advice on locating individual tickets, and a discussion of passes in general, www.seat61.com

As to your itinerary, I love trains but I wouldn't want to spend my entire vacation riding them.

From this, I take it you have friends/relatives in Lauda you will be staying with for a while.
Spend some time at www.bahn.com to see the travel times you propose. You'll see that many are impractical/impossible. Example:

April 9 - Arrival @ Munich (9am) going to Lauda Koegshonifen – @ 11 AM – 2 PM
3 PM Lauda to Bonn then Bonn to Lauda (up to midnight)

It is 4 hours travel time Lauda to Bonn. By the time you get to Bonn, you are already too late to get the last train connection back to Lauda.

Wow! This sounds like a marathon that you’re attempting in a sprint! For the time you’ll be in Germany, you’ll waste precious time (and money) traveling from city to city allowing no time to savor them. I would not take the time to visit visit Prague or Austria but concentrate on Germany. Berlin should get a minimum of 2 full days as should Munich. I like the suggestion above regarding visiting smaller towns. If visiting Rothenberg, consider visiting another town on the Romantic Road such as Dinkelsbühl - charming but much less touristed. I would drop Frankfurt for the history of Nuremberg and the old city of Bamberg.

Though I love traveling by train, if you do choose to see some of the smaller cities and towns, I’d also recommend renting a car for that portion of your trip.

I haven't purchased a rail pass since at least 2000. Over time the rail passes have become more and more expensive. To afford them you have to reduce countries and travel days. I've found the cost per day of a pass is only good when compared to VERY long travel legs. Since one of my lessons learned, over years of trial and error, is keeping your travel days/legs short makes a much more comfortable/enjoyable vacation.

Long story short, in your case I'd look at point to point and most likely just buy a ticket or make use of the Lander (umlaut over the a, means state/province) and Schoene Wochende (again with an umlaut, means nice/beautiful weekend) passes. I've been focusing on different countries for the last few years so don't know the latest details but they are great for getting around by train in Germany when you're on vacation.