Is taking an interest-bearing loan considered a necessity for repairing a house damaged due to a person seizing its garage, and the expulsion of this person who claims a forged contract exists?

The situation mentioned does not rise to the level of necessity that permits forbidden acts. Necessity is that which entails destruction, loss of a limb, prolonged imprisonment, or chronic illness, and it is not merely a hardship.

There are other means to remove injustice, including: your father taking action to reclaim his right, resorting to the courts, or maintaining the current situation until the cost of repair can be afforded through non-usurious means, or reaching an understanding with the person concerned.

An usurious loan is never permissible, even if you are in need, for Allah has facilitated other ways, such as borrowing from relatives, or Tawarruq (buying a commodity on installment and selling it for cash). "And whoever fears Allah – He will make for him a way out and will provide for him from where he does not expect."