Is it possible to 3D print sharp objects with high details? And how?
Best option for something like this would be to use an SLA printer. They can do sharper image detail compared to FDM style printers.

That being said, printing something like this poses its own set of challenges. In order to print a part, some surface needs to be in contact with the built platform, and depending on which surface chosen, you will end up with having some amount of overhang, or undercut. Not an issue in and of itself as these can be supported with support structures. For the size that you're looking at printing though, removal of the support material will be a bigger challenge. 

As for costing of this, that's not something that this forum is used for, but these structures don't look absurdly difficult to print. If you were to contact a local print shop, or check on Google for an online print house, they will be able to give you costing on printing these.