The patches of eczema on my hands are deep red. Will my skin ever go back to its natural color?

Yes. When a person is suffering from eczema, a patch of eczema is typically red and inflamed. With treatment and moisture care, the patch will typically resolve. It may resolve with a temporary darkening of the skin. With treatment most patches of eczema will resolve with time.
Yes. It might take some time, but if you protect your skin from drying out, and avoid using too much topical steroid, the redness will improve over time. Try applying vaseline (petrolatum) and wearing cotton gloves at bedtime to help repair the barrier function of your skin.