Is the husband obligated to pay the dowry for Hajj to his wife who requested a divorce due to her sexual desires not being satisfied, and he discovered that she does not fast Ramadan and committed adultery?

You are obligated to pay your wife's full dower if you divorce her after consummating the marriage. Her right to it is not forfeited by her committing grave sins such as adultery or abandoning fasting. However, you may initiate Khul' (dissolution of marriage at the wife's instance, often involving her giving up her dower) with her so that she may waive the dower if her adultery is proven. You are not entitled to accuse her of adultery unless it is proven.