Re: "Dent" on Hallway/Living room corner
From the picture it looks like the corner was originally done without a corner bead. I would recommend that after you cut an install th patch as described above and pictured here that you install corner bead from floor to ceiling. If it had been installed originally it may have limited the damage.
Also if you are holding a security deposit, make sure you photograph all damage and document all repairs and file it away.
Be sure you live your life, because you are a long time dead.-Scottish Proverb