Got my GC few months back with company A
Company A let me go and I joined  company B on GC
worked for company B for around 6 months as a contractor
quit the job and now going to visit Nepal for 4-5 months.

1. Am I all good to go visit Nepal for 4-5 months? Do I need to notify USCIS or DOL or have to follow any rules? Hope it will not affect my GC.

2. How can I file the unemployment benefits? I would be in Nepal for 4-5 months. During that time am I eligible to get unemployment benefits?

Appreciate your suggestion.

No u don't have to follow any notify USCIS or DOL about your travel and it will not affect your GC.
If you quit your job and now travelling to Nepal for few months, it's very unlikely that you are eligible for unemployment benefits unless you come up with the best possible reason of quitting the job and going to Nepal which could again be not good enough reason for the officer.

You should be fine for 4-5 months in Nepal
But how can you expect to get unemployment benefit when you quit the job, and going to a vacation. Are you trying to say government needs to pay for your vacation?
To get the unemployment benefit you need to be physically present in US and prove that you are actively looking for job.

Thank you ny2 and sajhamitra.
I was not aware of unemployment benefits rule.
One more question
While I will be in Nepal, do I have to have my health insurance covered?
If Yes, Do I qualify to enroll in the government provided health insurance? That could be cheap considering I would not have any source of income.

If you quit your job, you cannot file for unemployment. if you are laid off then you can file for unemployment.

damn..ramro job thiyo..i just quit..but no regret..
thanks mno.