Well if you are very sure of her dates and she had got normal monthly cycles, then the appropriate date might be 37 weeks.The ultrasound
dates can vary plus or minus 3 weeks in third trimester, so dont worry. Rather if you calculate the dates from the first trimester, they are the the most accurate of a variation of 1 weeks.
I think if the rest of the USG parameters are normal including a normal biophysical profile
, there is no hurried indication of caesearen section . Elective C-section is a option if you want ,and you can perform it now or after a week as you desire i.e 38 weeks, and there will be no problem with the fetal maturity since we assume 37 completed weeks as term if the lady is sure of her dates having a normal monthyly cycle or as calculted from her first trimester scan.
As regards placental grading, I think its a subjective finding that can vary .Well a grade 3 placenta is expected at your gestational age
and nothing to worry about it. Good luck,bye