Child custody includes two aspects, physical custody and legal custody. Physical custody means the right to live with the child. Legal custody means the right to decide on legal and welfare issues of the child.
Normally, joint custody means that parents share both the legal custody and the physical custody of their child. If the parents can share equally the time to live with the child, then most courts will not require child support from either party. However, courts will concern whether one party intends to use joint custody as a tool to evade his or her obligation of child support. Thus, if one party only can take 30% of the childcare, a court may still require him/her to pay child support to the other spouse, who is the primary child-care giver.
Some courts also would allow separation of the physical cusdoty and the legal custody when granting joint custody, if sharing child-care equally is not feasible between the parents. For example, parents live in different geographic areas. Under this situation, a court may grant both parents the equal right to make desicions with respect to the child's welfare; however, grant sole physical custody to one parent. Usually, the non-physial custodial parent must pay child support.
The visitation right is a separate issue to child custody. Even if you lose child custody, in most cases, you will have the right to visit your child regularly.
You always can ask the court to change its previous decision regarding child custody, regardless of the current status, joint custody or sole custody. Of course, it is another issue whether the court would change its previous decision. You have the burden to show that either yours or your spouse's situation has changed substantially.