Statto has explained it above: we have 82 points, and the most City can get is 87. So if we only get 5 points, they could theoretically catch us and win on goal difference.
Yep, at the mo we need 6 points, however City draw against Arsenal then we need 4 points, City would still be able to reach 85 points, we'd be on 85 points with a win against Everton, as mentioned we're +8 better GD than City.
City play Burnley the day after the derby, so we beat Everton, City draw against Arsenal & Burnley we'd be champions before we play Palace.
As unlikely as it seems, i have a funny feeling if City drop points against Arsenal, we beat Everton, City drop points against Burnley to make us champions, so City players & staff don't then have to do the guard of honour when City play us.