Forgiveness

Luke 17:1-4

17 Then He said to the disciples, “It is impossible that no offenses should come, but woe to him through whom they do come! ² It would be better for him if a millstone were hung around his neck, and he were thrown into the sea, than that he should offend one of these little ones. ³ Take heed to yourselves. If your brother sins against you, rebuke him; and if he repents, forgive him. ⁴ And if he sins against you seven times in a day, and seven times in a day returns to you, saying, ‘I repent,’ you shall forgive him.”

In these Scriptures, is it referring to a personal sin against you or just a sin in general?

If it's speaking of a sin in general, does this mean we have the authority to forgive sins? 

If he doesn't repent, do we have to forgive him because it says "IF" he repents?

2 Corinthians 2

⁵ But if anyone has caused grief, he has not grieved Me, but all of you to some extent—not to be too severe. ⁶ This punishment which was inflicted by the majority is sufficient for such a man, ⁷ so that, on the contrary, you ought rather to forgive and comfort him, lest perhaps such a one be swallowed up with too much sorrow. ⁸ Therefore I urge you to reaffirm your love to him. ⁹ For to this end I also wrote, that I might put you to the test, whether you are obedient in all things. ¹⁰ Now whom you forgive anything, I also forgive. For if indeed I have forgiven anything, I have forgiven that one for your sakes in the presence of Christ, ¹¹ lest Satan should take advantage of us; for we are not ignorant of his devices.

Again, here we see where if we forgive, then the Lord forgives. It seems to be general sin & not personal. 

Vs 6, what punishment was inflicted by the majority? Maybe kicked him to the curb?