Am I more likely to get pregnant right after an abortionbecause of the cervix being open?

No. The cervix will be somewhat relaxed as the result of an abortion, but ovulation will not occur for at least 3 to 4 weeks later - by then the cervix will be back to normal.
Not necessarily. You can conceive again whenever you ovulate. Having an abotion does not affect that aspect of your fertility unless you have an infection. The sperm are extremely small and can make it through a cervix without having had surgery to open up the cervix. So, your fertility is the same.
Clarification. You would want (not would not want) to wait until your doctor tells.
NO. No that is not true, and you would not want to wait to have intercourse until your doctor instructs you it is safe, and if you do not want to become pregnant, your doctor can offer you many birth control options.