Can taking estrogen pills and birth control cause any health problems?

Yes. Yes, definitely. However, the side effects are relatively uncommon and the benefits can be very great. The greatest risk of the pill is deep vein clots which can be very serious. The prevention of pregnancy (which itself has many risks) can be considered to balance this risk, and the pill also has long-term benefits in decreasing the risk of a number of female cancers.
Uncommon. Most people take birth control pills without any problems.Al medications including birth control pills have risks.Birth control pills have a slightly increased risk of blood clots, although there is not as high a risk as there is during pregnancy.Birth control pills also have benefits including regular, lighter and less painful periods, less risk of anemia, lower risk of ovarian & uterine cancer.