Yes it's possible. You should test now because since you missed 3 going on 4 periods it's likely your actually a few months along. You need to go into your OBGYN and get an ultrasound as well to find out why your missing periods.
I agree - its possible but very unlikely.
A HPT will be accurate about 14 days after conception so you could probably test now and then retest in a week if its negative.
In any case, if you have breast discharge you need to see a doctor to find out the cause (pregnancy or something else).
yes, it's possible. 1 in 200 sterilisations fail...so, unlikely - but possible.