Yes. Yes it is. The x-ray tech should give you a lead apron to place over your belly to protect the baby, and the amount of radiation used for dental x-rays is relatively low. The deep cleaning should not affect your baby at all. In fact, many dentists recommend dental cleaning during pregnancy, because the change in hormones can make your gums more susceptible to gum disease.
Absolutely. There are many misconceptions about dental work, x-ray radiation, laughing gas while pregnant. There has never been an association with dental x-rays having an effect on a developing fetus. As a general rule, wait until the 2nd trimester to have any procedure if possible. Have a cleaning every 3 months. Dental x-rays, although completely safe, should be reserved for those absolutely necessary.
Yes and no. I would get approval from your ob/gyn prior to having xrays. The amount of radiation exposure of dental xrays can vary depending on the number of views needed, whether or not digital or film is used, and the type of collimator on the xray tube. Xrays should only be taken when necessary and you must be protected with a lead apron with a thyroid collar. Having your teeth cleaned should be ok.