Ski hike in Dovrefjell in the first week of April

[Kaur Virunurm]

Hello.

We are a group from Estonia.
We plan a week-long, self-guided hike in Dovrefjell in the first week of April.
We will have moderately heavy backpacks (approximately 15 kg with with clothes, food etc) and backcountry hiking skis.
Thus we cannot cover very steep terrain or go over difficult mountain passes. 

1) Would this be a good time for snow conditions and weather?

2) Will the self-service huts be open at that time?
Do we need a DNT key, or will somebody be there for sure?

3) Could you give route suggestions for a 5-7 days long hike?
My current plan is to start and finish from Kongsvoll (train station).
We could also do a traverse (starting in Kongsvoll and finishing somewhere else). What options would we have? We need to get from the end of the hike to Gardermoen airport / Oslo.

4) Will the trails between huts be marked by that time? We can navigate unmarked terrain, but it would still be good to know about existing marking or trails. 

Anything else that we should know or consider in advance?

Sorry for writing in English,
and thank you in advance for any information!

Kaur