Yes. Minimal. Women walk out of the office after an amnio. From the mother's point of view the recovery is no different from having gotten an immunization - a little soreness at the needle site. Women should rest a bit if they are feeling contractions after the amnio, which is not uncommon for a short period of time.
Usually not. Most physicians allow their patients to resume their normal activities after an amniocentesis. Some physicians do recommend bed rest for a period of time after an amnio, but the studies show that complication rates are the same and the risk for problems is very, very low after an amnio.