Can you make your own models for weapons, armor etc in morrowind?

Of course. Many mods do this.
But you cannot do it in the Construction Set.
The most commonly used 3D rendering program for Morrowind is http://www.blender.org/.
http://niftools.sourceforge.net/wiki/NifSkope will also be of interest for you.
Both of these are free to download. And there are many other programs out there, too.


edit: http://www.gamesas.com/index.php?/topic/24-comprehensive-tutorial-and-useful-link-list/ from the pinned threads.

I suggest looking at A LOT of blender and nifskope tutorials, Blender can be the most confusing thing when you first start out.
http://www.blender.org/education-help/tutorials/

Also be sure to download Python 2.6, the latest version of Pyffi, and also nifscripts v2.5.5.

This.

I would personally recommend Milkshape 3d and LithUnwrap for modeling static meshes, like weapons and texture UVmapping, easy for a starter MS has a 30day trial and lithunwrap is free. Here's a good tutorial: http://detritus.silgrad.com/mstut_modeling.html

I can advise Sculptris. 3d sculpting implemented better here than in the blender. Very simple and free program. But after she needed retopo, which can be done in Blender.
http://www.zbrushcentral.com/showthread.php?t=090617