the rule is that the signature from your advisor has to be less than a year old. However, if you're in OPT, it's good (and highly recommended) to make sure that the sign is not more than 6 months old.

you said that it was signed in September this year, so I'm sure you don't need to get a new signature. Just go to the international services office at your school and ask them if you need a new signature. Pretty sure they'll say that you don't need one.

Being questioned/investigated depends a lot of times on the port of entry and the officer who "welcomes" you to the US. Here's an example: I(currently on OPT) recently went to Nepal and came back few weeks ago (POE was Chicago). My I-20 signature was recent and that's all the officer looked at, besides my passport. He didn't even ask for my EAD card or the letter from my supervisor/employer. And I had also made a mistake of forgetting to surrender my I-94 card when I left U.S. 

To all: Chicago seems like a pretty easy POE. I had mentioned that I was carrying some food items on the customs form and they didn't question me too much, neither did they asked to scan/open my bag.

Just check with your international services office for the peace of mind before you leave. Have fun in Nepal.