its the date on you gc. no if else or but. that is the date they backdated one year to the date you applied for GC. So just follow that date and wait for 5 yrs to that date. You can apply 90 days before the 5 yr mark date.
passport takes abt 3 months and yes you can go to nepal but if you filed an asylum you are not supposed to and someone might give your information to homeland since you posted this here. So good luck!