You already identified the problem: soil. It was probably overwatered a first, peat as you know stays wet for a long time if watered often. And since you left it completely dry, peat may have become hydrophobic.

Black is not a good sign, most often it's rot. Same with the leaves. If my plant, I would take it out of the pot ASAP. Get rid of all soil. Check the roots, cut of any damaged (broken, dry or rotted). Cut off rotted stems. Healthy parts could be re-rooted easily. Make a new potting mix that has good drainage, and use pot with drainage hole.

I can't see well where the stems are rotting, just going by your description.

thank you Rina. The stem is a little darker if you zoom the photos and take a look it is like little marks

It is very easy to cut up and re-root kalanchoe. That is what I would do if it was my plant. I recently did that to a kalanchoe I have for 6-7 (?) yrs. I periodically do that, throw away few stems and stick the rest into dry mix. They root well. I am not sure what else to suggest...Here are few that I cut up on Jan. 7th, not only rooted but blooming already:

Hi again. I have changed the soil checked the root and didn't have any signs of rotting. Still though, the plant looks miserable and the leaves are kind of falling . Also a small stem with baby leaf became very skinny and died ( looked like it was burned but it doesn't get direct light ) .

My main concern is the dark color , In some parts of the stem , is it normal? What about the yellowing of leaves.. I do not water it much :( Any ideas?

Plant with 'dark' stems is probably rotting, so repotting doesn't help. IIRC, I suggested to cut off rotting stems. I do not know what is exactly wrong with your plant, just going by your description...but I am thinking rot, since these plants are very easy to grow otherwise.