Yes, you'll get to see your children except in extreme circumstances. I have a Standard Possession Order which gives non-custodial parents fairly liberal access. If you add up the days, you have the children 35 to 40% of the time.
Generally, no a person cannot move your children without a Court's permission or your written agreement. This depends on what County you are in. In Dallas County, the Courts are much stricter about keeping the children in the County in which they were raised so that the non-custodial parent can have a meaningful impact on the child's life.