Hi, in this tutorial, I show how to identify a specific tile using the mouse coordinates:
Just use the player coordinates or pin a sprite a few pixels under the player to check which tile is colliding with.
For the slope issue, first make sure that the diagonal of the polygons are smooth when touching the polygon of an adjacent tiles, secondly make sure your player is a box and you pin the different animations to the box, because if you don't have a box (that is the actual player) and use only animations, their change of dimensions and collision boxes will mess up things.
Finally, for the mouse thing, don't use the mouse directly but create a sprite that is your pointer and set its position either to the mouse position or move it with the gamepad stick.
I would suggest to open separate topics when you have so many questions, it would be easier to get at least some reply about a few of your problem, rather than hoping that someone has time to go through all your questions :-)