Can you double check the Z-values of map game object and the player game object and their respective tilemap and sprite components? Remember that the Z-values add up, meaning that a game object with a Z-value of 1 with a sprite component with a Z-value of 1 will have a final Z-value of 1+1=2.
Also note that it is currently not possible to have sprites interleaved with the layers of the tilemap.
The stripes are most likely caused by texture bleeding. Change the “Extrude Borders” value of your tilesource from 0 to 1. It’s mentioned in the manuals and on the forum.