Is it permissible, in Sharia, to sometimes be frugal in spending on the family in order to save for the future, knowing that part of the salary is spent on household necessities, renovating parts of the house, or lending to some family members?

If your family is provided for and not poor, then there is no harm in saving your money for marriage. However, if they are poor, then supporting your parents is obligatory upon you if they are alive. Supporting your siblings is obligatory if they are poor, have no one to support them, no earnings, and you have more than what you need for yourself, and you are their heir. If you can combine supporting your family and saving for marriage, that is good.

If you fear falling into zina (unlawful sexual intercourse) and are able to marry, then marriage is obligatory upon you. If it is not possible to combine marriage with the obligatory support of your parents or poor siblings, then you are not required to support them.