Transport in Denmark

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Hello

I will be travelling in Denmark this June, for the first time.

I would really need some guidelines on traveeling around Denamrk with a fair amount of money.

I found this option of Inter Rail passes for travelling between cities:
http://www.gapyear.com/inter_rail/one_country_pass/1173574

As I will be visiting several cities, like Copenhagen, Aarhus, Odense and Aalborg, can you advice what can I do with travelling inside the cities? Is there a bus pass for several days for several cities, is it that in each city, there is a different public transport company so I need to purchase one in eaach city? How much is bus ticket or a 1 day pass in Copenhagen?

Are there bike with 3 wheels that can be rented?

Thanks

Free Spirit

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