Hello All,
I currently possess handwritten passport and I am a legal permanent resident of USA. I am going to Nepal on November 25, 2015. (The deadline as per ICAO is Nov 24, 2015 and my transit is only on Istanbul, Turkey). I was wondering if I can request/apply for new MRP passport during my stay in Nepal or do I need to have MRP passport ready prior going to Nepal. Any thoughts?

You need MRP to travel after Nov 24. No airports are accepting those handwritten passport. You might be sent back from US airport itself. So prepare yourself to get temp passport from Nepal embassy and apply for MRP asap.

teroobaau is correct. You will be returned from US airport itself. You can't travel to anywhere with that passport. It's too late for you to appy MRP at this time as your flight is Nov 25. Your best case scenario is good to DC immediately and fill the forms and apply for temporary passport. permanent MRP passport will take 3-4 months. Good luck!

Anybody know how long it takes to get temporary passport (travel document) ?

i heard 1.5 mnths but check embassy site for accuracy

1.5 months sounds way too long for just travel document.

I couldn't find anything on Dc-embassy website but in the UK embassy website it says 3 days.