The only part of your itinerary which I've done myself is the journey between Malmo and Copenhagen. It couldn't be easier. The trains run 24 hours a day, generally at 20 minute intervals. Both stations are fairly central. (In Copenhagen, one of the entrances to the Tivoli gardens is almost opposite the station). Many places in Copenhagen will accept Swedish currency but it would be wise to take some Danish banknotes with you.
You can download a brochure about rail travel in Sweden here:
http://www.sj.se/sj/jsp/polopoly.jsp?d=120&a=3 106&l=en&l=en#
(It's a pdf document. Use the 'zoom' feature, in Acrobat Reader, to study the map).
The home page of Swedish Railways is here:
http://www.sj.se/sj/jsp/polopoly.jsp?d=10&l=en
The official Sweden tourism website is a good place to start making your plans:
http://www.visitsweden.com/
Chris