Should I destroy this sick plant with coffee stained color leaves? The plant with drying branch, should I cut it off the branch? Please help me to make a right decision or to keep them healthy.

Is it a soil related problem? Still I am not able to mix the soil as I like (information from this website about soil mixture), only the available soil are container soil from the markets and coco fiber. I have been trying to get the right soil mixture. Furthermore, I did not press the soil tight when I re-potted these plants. Should I press the soil very tight if I do next time?

No. Loose soil is better than packed soil. The roots need to breathe as well as drink.

I wouldn't kill the browning plant or cut stems yet. Try popping the browning one out of the pot and see what's going on below.

They really don't look that bad, anyway.

How are you using coco fiber? The only way I ever use it is to line open baskets and to cover big drain holes. I wouldn't combine it with a commercial mix. What mix are you using, btw?

You will likely see a sickly looking plant a couple weeks after bringing it inside. Mine always look real good for a week or so with new sprouts and such. Then, after a couple weeks or so, they start losing most of their older/bigger leaves and begin to look like they are dying. My advice, snip the leaves as they brown. I would also snip the stems if they brown although I don't usually have problems with the larger stems. The one in the photo above would be one I would prune back to just above the next lower node.

If you are TRULY letting your soil dry out between waterings, then they should pull through fine. They won't thrive like they did outside in full sun 10 hours a day, but they will plug along until next spring. Just expect some leaf drop occasionally through the winter months.
And don't over water them.
Bruce

I would not cut the dying branch. If you cut it back, about all you will accomplish is it dying off further down the branch. If the whole branch ends up dead, I'd trim it back close to the base, but, not until it was totally dead / dried up. If the whole branch doesn't die, just leave it and it will probably put out new growth below the dead tip.

What conditions are they in? How warm, how much sun, water, etc?

When I brought mine in, I cut it back to the main stem - no leaves at all. I want it to essentially go dormant for the winter, and then start over in the spring. With no leaves drawing water up,I can keep the soil mix dryer and help prevent disease. I do have a few small leaf buds already, but they're not expanding, which is what I want.

I would trim that dying branch at it's base.
If the growing end is dead, then there's nothing for it to support and the entire branch is going to die back anyway. If it died from some kind of infection, like a fungus, then there is a chance it could spread down into the main trunk and kill the entire plant. Prune it just above the fork (so you don't damage the middle section where it could grow a new replacement branch from), and hit the cut with some H2O2 just to be safe.

Hydrogen peroxide? Do you do all your cuts this way?

I haven't had a stem problem with peppers, but rose canes can get infection or insects in through the cut end and hollow out the cane, so I tend to prune above where I want the new growth. I wonder if it would work for roses, too...

Normally I don't, but whenever the plant is clearly having problems I do.

My Butch T got pretty large, and it took a couple of days for the ends to stop bleeding. In the mean time the wet ends started to mold. Started spraying the ends with peroxide twice a day and it cleared right up until the plant was able to seal the wounds off. Kept it up for a couple days after that just to be safe. Its doing great now.