With that much time and that much rail travel take a look at railpasses and there are zillions of different types to chose from - single country passes like the Swiss Pass which can be a great deal if only in the country a few days and also because it covers many more things than say a Eurailpass valid in Swoitzerland would, etc.

And two-country passes, 3, 4 and 5-country passes and of course the Global Eurailpass that covers virtually all countries save the U K, which does however offer BritRail Passes - sometimes a combo on passes works best mixed in with budget air flights and regular tickets at times.

anyway for a great rundown on the European rail system and passes I always spotlight these IMO superb sources - www.budgeteuropetravel.com (be sure to download their free online European Planning & Rail Guide that gives loads of sample rail itineraries to consider) and www.seat61.com; and www.ricksteves.com - for schedules of any European train I always use www.bahn.de/en - the German Railways excellent online pan-European train schedule site.

With 3 months you could manage the Norwegian Fjords and some of Scandinavia.

Given your Aug-Oct schedule it makes sense to start in the north and work you way south.

Your southern Europe leg would probably be best served by starting in Barcelona and working eat along the Riviera to Italy.

Roughing something out;

Norway - fly into Oslo (probably expensive) or capital and then take an intra-European carrier to Oslo.
Copenhagen - you are already in Norway, right?
Czech Republic - Prague from Copenhagen, and Cesky Krumlov an Eastern Europe nibble
Germany - Regensburg Nuremberg, Bamberg/ Munich / Salzburg/ Alps/ Neckar or Mosel Valley (castles)
Lyon - from wherever you end up last in Germany having moves from east to west.
Barcelona - from Lyon, seeing Provence or the Dordogne on the way
Riviera - Nice, etc. snaking east from Barcelona
Tuscany - from the Riviera
Rome - from Tuscany

You might want to end in Rome, having obtained your beach fill in Barcelona and the Riviera since your best return flight option will probably be from Rome and going farther south means coming back. Still an option, though.

There is actually a direct train from Arhus, Denmark to Prague - I was shocked a few years back to see that train roll into Arhus - just a few hours from Copenhagen on what now is a main rail line to Germany.

But I would advise that you head to Berlin and spend some days in that amazing place and then go onto Prague. There is also an overnight train I believe between Copenhagen and Berlin.

Yes Potsdam, a shot S-Bahn from the center of Berlin is fantastic - the Prussian Versailles as they call Frederick I's Sans Soucci Palace - lovingly set in a huge park dotted with collies and whimsical structures, some representing afscination of that period with Chinese architecture.

Tuscan region for food and wine - great choice! I have been there last summer and Tuscany was beautiful especially the vineyards and old olive mills etc. These guided wine tours can be checked out on http://www.tuscany-cooking-class.com/wine-tours. The site contains other options like shopping, balloon rides etc if you are interested. Glad to help