Am I committing a sin, and is it incumbent upon me to inform my brother and repair his car, which I borrowed without his permission, after I caused a minor collision to it, knowing that I do not possess a driving license, and informing him might lead to significant problems?

Taking the car without your brother's permission and encroaching upon his property is impermissible, as Allah Almighty says: "And do not consume your properties among yourselves through falsehood," and the Prophet (peace be upon him) said: "Indeed, your blood, your properties, and your honor are sacred to you." You must repent to Allah and seek forgiveness from your brother. If he forgives you, then that is sufficient; otherwise, you are obligated to guarantee the value of its usage.

As for the collision, if you predominantly believe it caused damage, you must absolve yourself by informing him and seeking his pardon or guaranteeing what was damaged. The estimation of this should be referred to specialists. If you predominantly believe it did not cause any such damage, you are not obligated to inform him.