For the time being... (Assuming collision tile hotspot is at the top left)
To fix player falling into / hovering over the ground a pixel or two
+Player is on floor
+Overlaps Collision Tile
-Set Player.Y to Tile.y
To fix wonky left & right wall collisions
+Player overlaps Tile
+Player has wall to right
+Player is not mirrored
-Set Player.X to Tile.X
+Player overlaps Tile
+Player has wall to left
+Player is mirrored
-Set Player.X to Tile.X+Tile.Width
These might fix some of those other problems too.