I will be in Munich over Easter Friday, Saturday, Sunday, and Monday. Does anyone know whether museums and shops will be open or closed on these days? I am really interested in visiting the Dachau Memorial and Neuschwanstein Castle. Any help will be appreciated! Also any other suggestions about things to see that will be open over the Easter weekend. Thanks...

Most of the museums have websites with their hours and open days posted. I don't remember all of them, but I do know that I'm going to Neuschwanstein on Easter.

Shops are closed on Good Friday, Easter Sunday and Easter Monday. They will be open on the Saturday, to around 1 pm (small shops), around 4 to 6 pm (larger stores).
Both Dachau and Neuschwanstein are open every day during your stay. You should book the ticket for the latter in advance as a big crowd is expected at http://www.neuschwanstein.de/
There are many churches worth seeing, such as Frauenkirche, Assamkirche, Theatinerkirche and Jesuitenkirche. Nymphenburg Palace is a splendid Bavarian Barock building with a great garden, and fine museums include Alte and Neue Pinakothek (art galleries), Deutsches Museum and perhaps a beer in one of the beer halls.

You might also consider a visit to the Residenze in Munich, especially for the Ludwig antique carriage collection.

If you are interested in a free "concert", go to the Frauenkirche and catch the Hochamt (Solemn mass)on Easter Sunday. It usually starts around 9:30,or somwhere around that time of the morning. Even if you are not catholic, you would enjoy the music, if you are into religious classical music.

I will be in Munich at that time as well. In general, will restaurants/bars be open on Easter Monday? If not where I find some places to eat? Surely, the train station will have some thing open?

Munich won't shut down completely ;-)
There will be plenty of bars and restaurants open during the easter weekend. But shops will be closed.