Is the husband sinful for cutting off progeny because his wife refuses to conceive at a late age, and is he responsible for this action? And must he give his wife money for Hajj if she has not performed Hajj before?

Childbearing is a shared right between spouses, and the wife is not permitted to refuse it unless it causes her harm. The husband is not sinful if he refrains from procreation due to the wife's circumstances or for a legitimate interest. Giving the wife money for Hajj is not obligatory; rather, it is a charitable act for which the husband will be rewarded.