That is their natural state at his time of year. If you want a tidier look, cut them back. They will continue to bloom, but slower and sparser than in the better part of summer. I let mine go to seed and also clean them up so that they don't look so woe-begotten. I will also pull up the worst looking ones, knowing that the seeds are going to produce more next summer. I have not purchased seeds for at least 8 years now. They always come back and if I don't like where they are, I move them. Mine are primarily in pots that I seldom water, just like sedums. They adore full, dry sun; still, they reach a point when they are simply "done".

Yes, under the spent flower there will be a little capsule, like a little hat, filled with tiny roundish black seeds. Like pepper.

I think you mean Portulacaria. Yes, this one doesn't want damp soil to root on - remember it's not in the Crassulaceae, like your jade is). Cut it, dust with rooting hormone, set aside for a few days, plant in dry soil, and mist only until you see new growth (likely in the spring).

Hi, I have used portulaca for many years. and they almost always do that at the end of their season. It is a little early in the season now for that now, but nature has its ways..... I like to use the sambac vairities of purslane, the large purple flower, they last longer, I have one garden where they have been the ground for 2+ years now.