The one month pass allows travel for 30 consecutive days.  If you have it validated in Europe (before you get on the first train) on June 15 it will be good through July 14.  Since you wouldn’t validate it until you were ready to leave Paris and wouldn’t need it after you arrived in Rome (buy a point to point ticket to Naples) it would cover a trip of about 6 weeks. 

There are also flexi or select passes that are good for a certain number of days of rail travel in 2 months.  You could buy a 10 or 15 day pass and use it on the days when you’re taking a single long, expensive trip or several shorter trips that add up to the cost of one day of the pass.  Buy a point to point ticket for any trip that costs less than that.  For most itineraries this works out cheaper than the global pass.

For travel to/from Prague, use your railpass in Germany and buy a train ticket to cover the distance between the Czech border and Prague.  Bratislava is only a few km and less than an hour from Vienna. You can take either a train or the bus for this trip.

The pass is not generally good for local transportation.  You can use it on local trains so it sometimes helps getting around a metro area, but you usually end up taking buses or subways that aren’t covered.

A 4 country pass for France, Benelux (counts as 1 country) Germany and Austria might work for this trip.  Buy point to point tickets in Czech Rep and Hungary, between Vienna and Bratislava, for the tiny bit of Denmark (or if that proves to be too expensive add Denmark as your 5th country) and in Italy. 

Try putting your itinerary in www.railsaver.com  Follow the “I have a good idea of my itinerary” route and click “I prefer to purchase railpasses (as opposed to point to point tickets) ‘only if it saves money.’”

To answer your specific question regarding Copenhagen: Yes, it’s covered. In Copenhagen the “S-tog” and regional trains are covered, the metro is not covered.

I completely agree, check out railsaver.com, it saves a lot of time and stressing about which pass to get/is best for your plans.

The other people have covered the pass pretty well. I’m writing to let you know that your itenerary seems too packed. I truly don’t see you been able to visit all those places in 1 month without spending a day or two in each city. The big cities such as: paris, hamburg, berlin, prague, budapest, munich, zurich, milan, and rome, normally require 4-5 days atleast for one to actually get a feeling for the city and have it be a great memory. If you’re just going to go around looking at 2 or 3 major tourist attractions in each city, when you come back you might feel like you saw nothing. I would reduce those 22 cities to maybe 10 or 11 to fully enjoy it and not be stressed out. Also, you’ve chosen cities that most aren’t an hour or two away from each other by train (whether it’s fast speed or not).  Thus, you have to accommadate for travel times. Sometimes train rides can be as much as 16-23 hours! Or if you don’t do trains, even by plane it takes a while. 2-3 hours from long distance cities and probably 1-2 hours of airport time. Multiply that by those 22 cities you want and you’ll be lucky if you spend a day in each city.

Have fun!