Yes, gustav05, you did it correctly. There are several things which might not work here. Check the console output whether the texture was loaded, otherwise adjust the path.
If the model stays white you might have forgot to UV map your model. You need a proper 3d tool for this purpose. Adding a texture later on is also not a good idea because 3ds supports textures from within the format. So texture your model correctly and just load the model. Everything else will work.
If you also want vertex colors (no textures) you need the 3ds patch.
Yes, but if you did so you do not need to add the texture manually. It is loaded automatically by the 3ds loader. You just need to put it into the right location (best would be to use the same directory as the 3ds model). But just check the console log, it will have some important messages for you.
Yes, just use getMesh("mesh.3ds") and everything happens automatically (ok, the other code of your example is required as well, except for the manually applied texture). If it does not work maybe upload your model or send it to me directly. But please: Check the console log and find whether the texture is loaded or not.