It looks like your texture settings are fine (no compression, no texture filtering), but you may need to reimport the texture for those to take effect. If that doesn’t help, check the settings on the map prefab made by ST2U just in case. Beyond that, I can’t help, maybe others can, and you might have better luck in the Unity community.
As for the second issue, sounds like you should consider a Tiled upgrade xP What version of Tiled are you using?
Lastly, your tileset image seems to just be your map image? If your maps are all like this and this isn’t just a test, you probably don’t actually need to use ST2U, you could import the maps as background images directly, and build the collisions, etc using Unity. Rendering a single image without breaking it up into little tiles first would probably be more performant.