Is your cervix low and open in the early stages of pregnancy?

NO, HIGH/CLOSED. In early pregnancy the cervix is closed and 'fairly high' in the vagina unless there is 'significant pelvic relaxation' from previous vaginal deliveries . If the cervix dilates in early pregnancy, then a miscarriage may result. This problem usually occurs ~14 weeks and is referred to as 'incompetent cervix'. Because the baby is well protected, sex is ok in pregnancy unless there is a complication.
Not normally. The cervix should be relatively thick (>35mm) in the early stages of pregnancy. A short cervix increases the likelihood of a premature delivery. If the cervix is open, the risk is much higher, and may warrant the placement of a cerclage to hold the cervix closed until about 36 weeks.