It would fall under animated illustration (lots of different styles) imo.
As for costs best ask the people on here who do this (it won't be particularly cheap mind) but if it's for something you'd like to get done then putting up a brief in the tenders section (link below) and asking for quotes would be the way to go.
2D character animation but as Levi says, it's an "animated illustration" so the illustration and characters would have to be made with this in mind as it would be very difficult to animate a flat image.
(All the parts need to be constructed separately like limbs, head, facial expressions and so on for animation.)
As for cost....A lot depends on the length, style and complexity of the animation and how many different scenes/shots.
Also, the quality and experience of the Illustrator/Animator.
There are just so many variables that it's very difficult to answer that but it is quite a laborious process so it wouldn't be cheap unless you found someone that is looking for experience and happy to do it at a lower rate.