Is the roof tax due on the deceased father's house considered a debt that must be paid, or is it permissible to postpone its payment despite the accruing fines, especially since the questioner is currently unable to pay it?

If the loan was usurious, then you must repent and seek Allah's forgiveness. If the taxes are legitimate, they must be paid from your deceased father's money if he left behind inheritable wealth. However, if they are illegitimate, then you are permitted to evade them by any possible means.