I have some dolls with the same issue. Years ago (around 1998 or so) when I discovered my dolls like that, my mother actually called Mattel's customer service number and at that time she was connected to someone who told her that they had heard of it before and what it was unfortunately is the plastic changing. I know older dolls this happens to as well sometimes as the oils change in them and they can sort of get sticky and get dark oil dot spots. Here are my answer and opinions based on my own Barbie dolls, so take it for what it is worth, free

1) No, it will not spread to other dolls, it really is about what the doll leg is made of, nor will it spread to body, etc. I have found it only on the legs and my dolls all lived together (about 20 or so) in the same rubber maid box under my bed for YEARS before I discovered it and they were stacked on top of each other. It seems to affect a particular series of years, as my dolls between a certain set of years seem to be affected and others are not. HOWEVER, I did separate them as extra caution diseased and non-diseased once I discovered it.

2) Something I have found, is that if yours seem sticky or tacky wipe them off with a clean wet washcloth and let them air dry. Air seems to help sticky things in my experience with my Barbies and also my SSC dolls and minatures.

3) As a precaution if they will be stored in a box, I would wrap their legs in tissue paper.  When I discovered my own diseased dolls one of mine had her fake leather boots stuck to her legs. I have had issues with Barbie's painted leather jackets (such as Dance Club Barbie and sadly Sensations) having the paint peel off and stick to the doll or doll next to them and damage the other clothes. So I have now removed and bagged any painted item so no other clothing gets damaged.

NOW for some free thoughts as to why this happened:
1) I have some wondering if heat is a component to why some people have had it happen to their dolls and some have not and it is the same doll. I live in California, it gets to 100 or a bit more. I have not had air conditioning until recent years and my dolls were already damaged by then. They all lived in a plastic box. I can only guess what degree it was inside the box if it was 100 in my room.

2) The plastic used at the time. I have wondered if the legs possibly were made with some form of Silicone that was an issue. I know it is a broad category of synthetic compounds, but for any of you that are old enough to remember, there were issues with silicone breast implants from the 80's with lawsuits, recalls, and issues with them leaking/breaking down. (Yes, I know, a possibly far out there idea) So perhaps poor Barbie may be victim to the same issue? There was a LOT of different plastics being introduced into the market back then, and only time tells us what actually survives over the years.

 

I actually still have mine. They were sold just about everywhere as little trinkets back then. There were so many different ones. I have an album that they go in as well. I will try and find the album and take a few pics tomorrow.

That doll has the wrong eye color used for Jasmine, Pocahontas or Mulan. Melody dolls (Ariel's daughter) were hard to find and were only released at Toys R Us, and they do not look like her either. It could possibly be an Esmeralda doll, since she would have that shade of eye color and dark hair. Although, judging on the eye shape alone, since it has almond eyes, that is more typical of Jasmine even though it is the wrong eye color.