Question 1:
There were effectively two possible choices throughout the film - Plan A and Plan B.
The former involved Dr. Brand solving an advanced equation which would allow human beings to truly harness gravity. Doing this would allow NASA to launch a space station, complete with everyone on Earth, into space.
The latter was relevant if Dr. Brand couldn't complete his calculations or the Endurance sent no word back/found no suitable planet. NASA had a bank of human embryos designed to ensure all humanity could survive (effectively giving up on the people on Earth). The idea was that the Endurance team would find the most habitable planet, raise a generation of these embryos and thus they could raise generation after generation themselves.
In the film, when Cooper leaves the Tesseract, he has provided Murph with the data needed to make the equation work. Thus, Plan A is the option they follow. Cooper Station's construction was not possible before Murph solved the equations. Therefore, I believe it's effectively a type of ark. It could be increased in size to accommodate all of humanity. Or, more likely, multiple arks have been (or will be) built to accommodate humanity.
To me, this seems logical given that we know Earth is not suitable for human survival any longer. I would probably suggest that humanity is still in the process of coming out to the stations, as Cooper is effectively told to go on ahead.
I would assume this is why they don't jump ahead. For now, they can wait on the other side of the worm hole whilst a) humanity leaves the Earth and b) whilst a new home is sought out on the other side of the worm hole.
Question 2:
The worm hole is very much still active. We know that at the very end, Murph tells Cooper to seek out Dr. Brand as she's all alone (suggesting strongly they've received some information back through the worm hole from her. Additionally, as she tells him to seek out Dr. Brand, the worm hole which will enable this must still be active.
Question 3:
As the worm hole is still open, Cooper is going to it to seek out Dr. Brand.
Edit:
Upon rewatching the movie, I noticed that when Cooper wakes up on Cooper Station, his doctor mentions Murph is on route from another station - this definitely means there are multiple stations. Whether they are all orbiting Saturn, and the wormhole, or whether they are scattered, is still unknown.