I tried to upload your sample and didn't reproduced the missing textures problem. It should'nt be a problem since we keep all the textures that are zipped with the model (even if it doesn't use them).
For the tiling issue, I seems to be related to the way materials and mappings are defined in Showcase. When editing your materials, you can choose to use model's UV coordinates (that are actually stored in the .FBX file), or some mappings that are set by Showcase at render, using this dropdown menu :
It looks like you use Triplanar mapping for the sample. Setting the mapping type to Parametric(UV) will use the UV data from the FBX, and lead to the same result as the one you get on Sketchfab. In our side, UV coordinates are the only data that we can have to map the textures.
A possible workaround would be to set the mapping of your models before exporting to FBX, in order to get a good result with UVs. Texture baking can also be a solution for you to reach this goal.