If one is married for 10 years can the woman claim Spousal support if she is going to School full time Husband does not give child support either?

The laws vary from state to state.

Speaking in very general terms (without knowing the state), 10 years is considered a long term marriage, and spousal support can be awarded. If a wife is enrolled in school the court may order that support continue until her education is complete (in a reasonable period of time) and for a short term after that until she can become gainfully employed.

There are numerous settlement options though, spousal support is awarded in some cases until remarriage, and in some cases not at all. Spousal support is generally determined by the assets of the marriage, standard of living in the marriage, income of both spouses, and the length of time of the marriage. There are instances where a wife is the earner, and she is ordered to pay support.

Child support is for the child, and is determined by the courts in the interest of the child and the laws vary from state to state. Generally speaking support payments are often ordered to the parent who has primary custody. Today it's not uncommon when both parents are earners of relatively equal levels who share 50/50 custody to have no support order (but to have ordered expenses: IE one parent pays insurance, another parent picks up dental, one parent picks up sports costs, etc.)