What is the ruling on using others' tools and possessions without permission, what is the expiation for that, is it obligatory to seek absolution from their owners if they were consumed or damaged, and is it permissible to postpone seeking absolution?

There is no harm in taking things that are customarily taken among friends, especially simple items, because this is permitted by custom. The intent is that which the owner willingly consents to, based on the Almighty's saying: ﴿There is no blame upon the blind, nor any blame upon the lame, nor any blame upon the ill, nor upon yourselves, if you eat from your houses, or the houses of your fathers, or the houses of your mothers, or the houses of your brothers, or the houses of your sisters, or the houses of your paternal uncles, or the houses of your paternal aunts, or the houses of your maternal uncles, or the houses of your maternal aunts, or [from houses] whose keys you possess, or [from the house of] your friend.﴾ [An-Nur: 61]. As for what is taken without permission and without the owner's willing consent, it must be returned to him, or given in charity on his behalf if it is impossible to reach him.