I've never heard the term "dropped" used before. Your placenta doesn't move, so it can't drop as far as I know. Your placenta implants in your uterine wall-some implant lower on the uterus than others, and it is not terribly uncommon to be diagnosed with a "low lying" placenta or placenta previa (marginal, partial, or complete) at 20 weeks, which means that your placents is either close to, partially, or fully covering your cervix.
As your uterus grows with the baby, the place where the placenta is anchored may "stretch" to be higher up relative to your cervix, and the placenta previa is resolved (and should not lead to any complications)-think of a deflated balloon-if you make a mark with a pen near the bottom and then blow the balloon up, the mark does not seem as close to the bottom anymore, even though it hasn't rwally moved-make sense? It would be helpful to know how close your placents was relative to your cervix as close/marginal placentas are more likely to resolve than full placenta previas.
I was diagnosed with a low lying placenta at 20 weeks (and was put on "pelvic rest" i.e., no activities that could result in orgasm) until a follow-up ultrasound at 32 weeks. In the interim, I switched practices, they said the pelvic rest thing was bunk, did a follow-up US at 30 weeks, and the LLP had resolved.
As for your second concern-it is also not at all uncommon for a baby to be breech at 20 weeks-it has MONTHS to turn, why be in a hurry? Sorry you were disappointed not to find out the gender though-I like delayed gratification, so I didn't/don't want to know myself, but it's always disappointing when you can't get the information you desire. Better luck during the next US!
Wife to my DH Mama to my two girls '03 and '06 and my sweet 3-'10 I am blessed.