I made a travel plan from Munich, to Salzburg, to Cesky Krumlov, to Vienna, to Budapest,
to Krakow, to Prague, and then to Berlin.
When I looked at the dates of Budapest they started on August 20-24, 2016. I found that August
20-21 is a holiday and the next day is a Monday when places like museums are closed.

Are tourist places that we would want to visit open or closed on the August 20 holiday and are
they crowded?
Also is there a problem with taking overnight trains between Budapest and Krakow and also
Krakow and Prague?
Should I revise my trip plans and go from Vienna to Prague, then to Krakow, and to Budapest, and lastly Berlin?
I am going home from Berlin.

Have a look at www.budapestbylocals.com/event/august-20th/ It might even be a good reason not to miss it!

<<Are tourist places that we would want to visit open or closed on the August 20 holiday and are they crowded?>>

How can anyone answer this question when you don't say what tourist places you want to visit?

August 20 is the feat of St. Istvan, Hungary's National Day. Hungarians make a big deal of it, and I think you should regard it as a bonus. It's equivalent to visiting Dublin on St. Patrick's day (but with better fireworks).

You probably should make reservations for the train to Krakow ahead of time.