Is it permissible for the husband to request compensation for Khul' if he is well-off but incurred financial damages from expenses and gifts, and the wife requested separation for unknown reasons after the marriage contract and valid seclusion, but without consummation?

It is not permissible for a woman to seek divorce from her husband without a legitimate religious reason. As stated in the Hadith: "Any woman who asks her husband for a divorce without any fault, the scent of Paradise will be forbidden to her." If a woman dislikes her husband and fears falling short in fulfilling his rights, she may seek a divorce in exchange for compensation she pays him, as did the wife of Thabit ibn Qays (may Allah be pleased with them both). If the husband is not the cause, he has the right to refuse divorcing her except in exchange for compensation upon which they both agree. It is better to reach an understanding and refrain from divorce or khul', and to seek Allah's help and consult people of wisdom and reason.