When does a woman have to do Ghusl if her husband pleases her with his hand (gives her orgasm)? Is a menstruating woman allowed to please her husband with her hand or mouth?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

A woman has to make Ghusl (have a bath with the intention of purifying herself) when her husband has intercourse with her, even if there is no ejaculation from both of them or from one of them.

If there is ejaculation because of a desire while awake or asleep (without intercourse) she has to make Ghusl as well.  And she has to make Ghusl after becoming pure at the end of menstruation or after giving birth to a baby.  So these are the cases when a woman has to make Ghusl, apart from this she does not have to make Ghusl.

The husband can take pleasure from his wife during her menstruation (or after giving birth) without sexual intercourse in vagina or anus.

For the last part of your question, please refer to Fatawa about oral sex: 84137 and 81980.

Allah knows best.