Yes. If you have an abscessed and painful tooth that needs to be extracted, yes, it is best to have it extracted now so that the infection will not spread and cause harm to you and your baby. It is best to have this done in the second trimester. You should see your dentist for a complete diagnosis to see if the tooth needs to come out now or can wait until after your baby is born.
Yes w/ a caveat. You can get teeth pulled while pregnant, but there are a few important things to keep in mind. We prefer to take care of things like this in the 2nd trimester. First and third we try to avoid dental treatment if at all possible. But, if you're having a toothache, the chemicals your body is producing in response to the pain is worse for the baby than having the tooth pulled in 1st or 2nd trimester.
YES. If you have an infection or cavity it is recommended that you get it pulled as soon as it is found. Most pain medications, antibiotics and procedures are safe in pregnancy. An X-ray of your mouth is also safe if your belly is shielded. Leaving an infection may increase your risk of early labor, so you are best off getting it done early.
Yes. Unless contraindicated or prohibited by your ob/gyn doctor, you can. Not in first trimester, unless an emergency. Second and third trimester is usually ok, but not too late into the third trimester. Local anesthesia is ok, unless contraindicated for other reasons. Iv sedation, etc is not ok for elective procedures.