Nazuna campaign is special mission that appear every 7th day and 27th day of every month.
When it appear notice will popup and it will live for limited time (Don't remember how long).
Since your play for 2 months you should already do it.

Special quest campaign is just like it name.
Dev will annouce when it available.

What you have to do to fullfill the quest is something like clear any mission for ??? time.
Gathering for ??? time. Clear whale mission for ??? time etc.

And I think the new Nation defence also give you D-medal as full clear reward, not sure about it.

Last thing, D-medal is one of the rare currency for F2P. It's hard to collect, becareful before trade it in shop.