I had renewed my passport from DC. I used FEDEX with tracking to send and return the passport. Unless you are in DC area, you won't have other ways to send passport unless you want to travel.
I don't recall sending originial citizenship or marriage certificate. But I don't think originials would be required other than your expired passport. 
As far as I know, a birth certificate is not required. You already have your passport.
The new passport they issue are MRP for which I believe, the embassy sends your expired passport to Nepal. So it will take few months. So you have to plan your travels accordingly.