Shadow/light issue that i cannot solve

Many things could the issue. At first some parts of the vase are not correct unwrapped and the texture have lighter grey colors (shown in the pictures). Yes maybe the specular map could be the problem.

In S4S, open up the object and select the "Warehouse" tab. You'll find 2 DST image instances (usually for each mesh group) with colors of some sort that don't look like your main texture, which are the specular and normal maps.

Most of the time I just extract them and open in Photoshop, pick what seems like the neutral color, copy a square of it, and fill the entire map (making sure to remove the old one so the new one is still transparent). There's probably a tutorial on editing them properly somewhere, though (I edit them as PNG and remove the info to simplify things, but you can use DDS files or edit them properly if you want your item to have a working bump/specular map).

Looks more like a texture problem, though. Is the problem as visible if you make the white parts entirely white?

The way this is mapped makes the seams not go well together at the ends. A trick I often use when UVMapping is to select a line of vertices, then click S (scale), X/Y (for vertical OR horizontal, not both at at a time) and 0, then press enter. This makes all the vertices line up. It's especially useful for cylindrical items or items where you want seams to line up on opposite parts of the map. Sometimes it also makes recoloring a bit easier, but with some meshes it can cause some stretching, so use with care. You can use it only on end vertices to make sure they line up, though. 

Also make sure the mesh is properly smoothed (with smoothing tools to fix normals, not with extra polys/faces!) and that the normals don't make a seam.

I think you need to make sure you use a neutral transparent texture (see-through) and NOT an invisible texture (empty texture) for the bump/spec, because there is a difference. One of the maps is pink/green, which I think is the specular map, the other one is grey and I think that one is the bump. I think bump maps usually have 128x128 white/black, and 0 for color as the neutral no bump color (that's what I'm used to from TS2, anyway) - but I'm not sure with the specular map. 

The mesh looks alright from what I can see (no normal issues). There are a few minor UV alignment issues, though. There is a small texture seam on the inside of the vase, but I'd say that's more likely to be the gradient and the UVmap not properly aligning. The outside looks fine with these particular stripes, but may not work with gradients and other patterns due to the same misalignments in the UVmap (that's why you want the end vertices to line up, so there isn't a seam). It doesn't explain the clear seam in the first picture. That's more likely to be a problem with the specular or bump, or something else. 

Can you upload the Package file, too? The problem could be somewhere there.

^ The link is to this topic, not to a package file.

Doesn't seem like the link works. I only get a page with a lot of random characters.

Not sure which site you're using to upload, but just so you're aware, some characters do weird things when they are in filenames. Besides ".package" at the end, the safest to use are Aa to Zz and 0 to 9 and _

Spaces and other characters can sometimes do a lot of weird things, so best leave them out. Some characters except for the ones mentioned above are theorized to have a negative effect on loading times if there are enough of them, and some the Sims games can have issues reading which causes them to not show up. 

I think it was because it's called kähler, but i changed that now. I'm using my own domain for uploading