When creating textures, does The sims 3 support normal maps?
(I would really want to use normal map if possible since it's good way to fake low poly to look better or have something that's not even there)

if not does it at least support just bumb maps?

yes, the sims 3 does use normalmaps.
You often find them in the mesh tab(TSRW and CTU)

In TS3, unlike TS2, normalmaps are tied to the mesh - so if you want to use an EA mesh with a custom normalmap, you'll have to "clone" the mesh by exporting and reimporting it if using CTU. I don't know how this works in TSRW; it probably clones the mesh automagically as part of its determined mission to create as much file bloat as possible.

I see. How does this work if I create custom mesh (not using any EA mesh) and custom normalmap? How Do I tie them together what is the method? (sorry, I'm still kinda of confused how this all works since I am still learning the sims cc creation.)

In CTU, you can import the mesh files and the normalmap (in DDS format) on the same tab of the window. This also goes for replacing/updating them - just remember to enter a unique name for your new mesh first (the box for doing so is also very conspicuously there on the same tab). In TSRW, you can replace/update/import (or clear) the normalmap by opening the Msh tab, and hitting the ... button next to "material".

Thanks!