What should I do to absolve myself from the exploitation of a rented apartment with an old, legally void lease contract, given my mother's and siblings' refusal to take any action regarding it, and is it permissible for me to pay for my personal use of the property with my own money to the landlord without my family's knowledge, and how can that amount be calculated?

The aforementioned apartment is usurped property and must be returned to its owner. Preventing the owner from accessing it is considered usurpation, which necessitates compensation for its benefits by the perpetrator. Usurpation is established merely by gaining control over another's property without their permission; simply preventing the owner from accessing their property is sufficient. Entering a usurped apartment is religiously forbidden. Therefore, the questioner must seek permission from the apartment's owner to enter it, whether for rent or without rent. He must also convince his mother and siblings of the religious ruling with gentleness and kindness.