a) Definitely doable, you can get a really nice hike in that time.
b) I assume you know about DNT and it is their huts you are talking about? http://turistforeningen.no/english/
They also have a page with lots of suggested hikes that you can have a look at: http://turistforeningen.no/english/trip.php?fo_id=3987
For example this one is spectacular: http://turistforeningen.no/english/trip.php?tp_id=4372&fo_id=3987
It's 4 full walking days, so you'd need for getting to and from start/end point. But it is also possible to shorten it by starting and stopping elsewhere.
http://turistforeningen.no/english/trip.php?tp_id=4373&fo_id=3987
Four days in Rondane, very nice. First day can be done by starting from Oslo the same day.
In the Hardangervidda national park, train to Finse, then walk between huts:
Finsehytta - Krækkja - Kjeldebu - Rembesdalseter - Finsehytta.
Can alternatively be shortened be going directly from Finsehytta to Kjeldebu.
c) I would check norwegian, sas, ryanair, british airways. Often possible to find good deals, it is a competitive route.