There is nothing wrong with a woman who is Junub cooking, looking after her house, taking care of her children or fulfilling any other needs.

If a woman sees in a dream that someone is having intercourse with her, this is something natural, for women may experience erotic dreams just as men do. If a woman sees such things in her dream, then if something comes out of her as a result of that dream, she has to do Ghusl.

It is permissible for a person – whether a man or a woman – who is in a state of major ritual impurity to touch things such as clothes, plates, pots, etc., before doing Ghusl, because this person is not impure and does not make the things he or she touches impure.

The most correct view is that if semen is discharged without desire, Ghusl is not required but you have to do Wudu. If the discharge of semen is accompanied by feelings of desire, Ghusl is required according to scholarly consensus.

Six things make Ghusl obligatory: 1- emission of semen, 2- penetration of the penis into the vagina, 3- when a non-Muslim becomes Muslim, 4- the deceased person must be washed, 5- Menses and 6- postpartum bleeding.

Anyone who becomes Junub (a state of major impurity) as the result of a wet dream or intercourse has to do Ghusl. If you cannot do Ghusl because there is no water available, or because you are unable to use it, then you should do Tayammum and pray. In your case, you have to repeat the prayer because you did not do Ghusl or Tayammum.

Ghusl is not required in the following cases: 1- every time one is going to meet people – it is encouraged to do Ghusl beforehand, 2- when undergoing any physical change, 3- for some acts of worship, such as doing Ghusl when entering Ihram.