Looking at a map of train routes would help you. Eurail have a map, but DON'T buy the Eurail pass. Off the top of my head, you could fly into Munich, go south via Austria to Switzerland, then west to Paris, then north via the Netherlands to Denmark, then cross over to Norway, flying home from Oslo.
The Man in Seat 61 is a great website for European train travel, and it is very cost-effective if you book in advance.
This is impossible to answer because we have no idea how long you are staying in each city nor how you are traveling to each city nor the type of person you are as far as what you like to eat, if you drink, what type of activities, etc. You need to provide those details.
10 days ... pick no more than 3 European cities. Your first one should be which ever German city you are flying into. Spend 4 nights there (first day to get over the travel/any jetlag) and 3 each in the other two cities - fly home from city #3. Any more than this will just be like being in an episode of the Great Race or a bragging opportunity to tell your friends "we've been to ..."
To make your decision, start with a map and then visit the 'things to do' tab in the green bar at the top of the forum home page for each city that interests you.
Excellent advice from thmoore.
No-one has answered your question about how much such a trip will cost because it is an impossible question to answer without knowing much more about you, your interests, your requirements for accommodation, and how much you drink!