Is the wife sinful for concealing from her husband the purchase of a house, and for intending to inform him of only part of her salary after her loan is paid off to help her family, knowing that the husband is extravagant and refuses to help her family?

Not informing the husband about the purchase of a house or the salary estimate is not lying; rather, it is concealing something that does not necessitate disclosure, and equivocation (tawriyah) can be used. The husband does not have the right to prevent his wife from helping her siblings with her money, and she is free to dispose of her money as she wishes. The husband is obligated to spend on his wife in a reasonable manner, and the wife is not required to spend on the household from her money except as a voluntary act. The wife's money is her exclusive right, and the husband is not permitted to take anything from it unless he stipulated that condition to allow her to work.