No, Magento 2 just isn't ready for it.
I recently checked it out and installed it but there is very much styling missing in the backend and everything is still subject to change.
I tried developing a module but finding documentation on it was difficult and many tutorials are outdated.
I would recommend waiting at least another year before you can properly use Magento 2 on a live environment. Right now they still seem to be defining Magento and transfering everything to jQuery. Also expect Magento to be buggy on it's initial release.
If you look at the history of Magento 1 you can see how long it takes to have it stable and reasonably fast.
However I do suggest you install Magento 2 just to have a look at what's changed in the structure.
Also I don't completely agree with some of the changes they've made, for example assigning products to categories. They got rid of the tree and now they have a text field that auto completes when typing the category name (like the tags on stackexchange). I would rather use the tree to navigate to a category to make sure I got the right one. It is, however, quicker to use as opposed to the tree.
EDIT
If I write own modules for Magento 2, is the module structure very
likely to change?
I would say there is a chance of them changing it, nothing that should stop you from developing a module though.
Are the core functionalities we have in Magento 1 already functional
in Magento 2?
I haven't checked this but because of the transfer to jQuery and the changes they've made to the core there may be bugs.