My feeling is there is no complete answer for this question unfortunately - that it's just up to the scorer.
For exapmle, on Saturday the Blackhawks and Blues played. Adding up the TOI for the blackhawks comes to 288:56, which is 11:04 short of a full game (of 300). However, there were 12 minutes shorthanded plus 2 minutes of 4 on 4 in that game (Kane/Pietrangelo unsportsmanlikes), for a total of 14 minutes of time that's not accounted for; meaning that you're 2:56 over the amount of time that should be accounted for. As Kevin points out in comments, those can be accounted for by looking at when the StL PP goal was scored - and the last minor was with only :04 left in the game. So the ToI does look like it adds up.
Looking at the shift chart for the game, I don't see any overlaps at all in the shift changes; they all have a corresponding off/on pair. But whether the TOI stat comes from the same place as the shift chart, I don't know.
As far as +/-, again I don't think it's explicit anywhere; it would be up to the scorer to determine exactly who was officially on the ice when it occurred. Typically when I've seen it, the player getting on the ice is credited so long as they're fully on the ice - the player leaving is more or less 'out of it' once that's happened.