Yes & yes, however:
Having a cyst or cyst does not prevent ovulation
and does not mean you can not get pregnant.
about one in every four pregnancies ends in miscarriage and having a history of a miscarriage does not significantly increase risk of a future miscarriage, though I advise all who have miscarried and all with ovarian cysts to have a thorough thyroid evaluation. See http://bit.ly/1qOnAA6