Is it possible to race against a previously recorded activity and know at exact points, how much time I am ahead or behind?
It seems that you can only know on the overall time and distance.
You can, but it involves turning that activity into a course. This can be done on the unit or in Garmin Connect.
If you then add the following data fields to a training page, Time ahead, Distance Ahead. This will give you the information you need. you can also enable the Virtual Partner training page. This will also give you the same information and also allow you to adjust the speed of the Vp.
One important piece to realize is the Virtual Partner's time / distance vs you includes any time stops for the VP. i.e. if when you recorded the track, you stopped for a traffic light, or maybe to each a munchie on a longer mountain bike ride, that is included in the previous performance. Let's say this time when you race it you don't make the same stop, as you cross that point in the course your time ahead will jump forward by the amount of time you were previously stopped. The distance ahead calculation then gets a little backwards. Garmin's algorithm for this stuff is funky for some reason. Seems like it would be simple math but they did not get it quite right.