It doesn't look like there will be a new continuation to Gemini, but there's a lot of talk online about a third season which is a prequel that takes place in South America during the Heaven's Gate incident.
As to your other questions, they are all answered in the anime. The first season provides a good foundation for understanding the series, but in order to understand the conclusion for Gemini, you need to pay attention to the dialogues in the OVAs and then you should probably re-watch Gemini, and then your questions should be answered. As opposed to popular criticism, the series answers many of the questions most people end up having, which you might have as well. Basically, imagine that the Dolls are like a flood like in the popular story of Noah's Arc. They are constantly evolving (notice how much Yin changes) and are sent to replace humans by a higher being (notice Heaven's Gate and Hell's Gate, those weren't used just because they sound cool).
Contractors are like failed Dolls. They are rational like Dolls, but too full of emotions like humans. That is why Yin, who turned out to be the most evolved Doll, was trying to fulfill this purpose of replacing humans. None of this is outright told to you, it's all implied from specific conversations (most of which are in the OVA, especially the last 10 minutes or so of the last episode, and the second season, not the first).
As to who the boy is, if you note in the second season you will find out that the red-haired girl is a clone to her twin brother who is a contractor. The only thing is that his clones aren't perfect, such as she was cloned as a girl and not a boy. The boy that appears at the end is a clone of Yin (notice it's not perfect clone since it's a boy) which is the spawn of the new world, which is why they wanted the boy to start off with.
This development of Dolls replacing humans as the next form of evolution in humankind's history is similar to Elfin Lied, where people are to be replaced by the creatures in the show, and Guilty Crown, where the next form of evolution for humans is an immortal, crystal-like form where the consciousness and memories of humans will reside.
There's more to be explained, but I haven't seen the series in a while so I just recommend re-watching it, and just remember that most of your questions will be answered. Just pay attention to the conversations held and not so much all the action scenes. PS: I'm pretty sure the manga Darker than Black: Shikkoku no Hana is set after season one and before the OVA, it's not a replacement of Gemini. Also, you could read it because they talk a little about the evolution of the Dolls in the manga for a bit.