Does the husband have a share of his wife's salary based on their agreement to share ownership after marriage? And is it permissible for him to stipulate a share of her salary in exchange for his allowing her to go out to work?

There is no objection to marrying a rich woman. The Prophet, peace and blessings be upon him, affirmed people's consideration of wealth, beauty, and lineage in marriage, and encouraged prioritizing and valuing religious devotion.

However, an agreement to share money is invalid if it is combined with the marriage contract, as jurists prohibit combining a partnership or sales transaction with marriage in a single contract.

If the marriage is concluded with its conditions, and then the spouses agree to share what they earn, this is impermissible due to the presence of gharar (definition) (excessive uncertainty) and jahalah (ignorance), which invalidate the agreement.

As for the husband stipulating that his wife give him a portion of her salary in exchange for allowing her to go out, this is permissible if her work is permissible and she did not stipulate permission before the contract. Otherwise, he is not allowed to take anything from her except what she willingly gives.