Altium 3D not showing textures
Step AP203 does not seem to preserve colors, whereas AP213 does. Not sure about "textures", but neither seem to support transparency. If you're just downloading random 3D files from the internet, maybe they're not exactly in the advertised format. 

For the ones that look like blocks, make sure that in the 3D body you've selected "Generic STEP Model" rather than "extruded", and of course you must embed and place it properly. 

Edit: with the further information -- You've got a collision there- perhaps you have the highlight color set to gray rather than the typical virulent green. Maybe you've placed the bodies so they intersect the PCB surface. Since you didn't make them - they might be made with a plane not optimal for Altium, and just need to nudged up a hair. Also make sure you reset error markers.