I am not sure how to get the metro ticket in the game, I there is some parkour that I don't know how to do

You'll have to drop off the ledge where Flynn is standing. There's a platform down there, and from there you can jump onto the train.

Tips for the following parkour section:
- wing icons instantly refresh your dash
- move the camera around with IJKL or the right stick on a controller
- check the area map to see the level layout