It is 90 days, and exactly 90 days, before your five years of residency that you are eligible to apply for naturalization. I don't have the exact link but if you go over uscis.gov, you should find it. According to it, because 3 months is not equal to 90 days, make sure your naturalization application package does not reach before 90 days of the date your PR card issued date reaches 5 years. Been through it, so I know. 

About the second question, I don't know what the law is but I have heard you can't buy properties because Nepal does not accept dual citizenship yet. You don't have to give up your Nepalese citizenship while getting US citizenship here, but once in Nepal, when you have US citizenship, your Nepalese ciitizenship is assumed void. 

But yes, you can be out of US for upto 2 years if you apply for a reentry permit. otherwise it's six months.