Could I create subcategories in K2 as well? If yes, could I add items in various subcategories and actually display them in the website?

Thanks and I look forward to hearing from you

Sure you can. Create a category, then create another and specify first category as parent.
You can display parent category's items and/or all items from all children categories as well.
You can also display only some selected categories' items.
You can bind a menu item to K2 categories(one or more selective) to show desired category items under that menu.

Thank you for your help. However, when I create an item, I can not select a subcategory which I have already created. Is there a simple way to do so?

Thanks

Why not? if you created AND published a category, it will appear under "select category" on new item's page.
Don't forget to publish what you created :)

Edited: well i was wrong: even unpublished categories will be shown under "select category".
Maybe you created ordinary joomla article? K2 categories are visible only for K2 Items, not for usual Joomla articles.

Yes, both category and subcategory were published. However, while adding an item in the K2 area, I can not select both category and subcategory. That is a problem

Oh, so you mean assigning multiple categories to one item. That is not possible by default, however if you install "K2 additional categories" extension, you can do that.
Or, choose to display parent category under appropriate menu item and specify to fetch children categories' items as well. This will not solve all cases however, so consider first option.

@Toda Namiki
K2 only supports one category per item by default as Zurab corectly said.

That said you do not need to add this item to both the category and the subcategory. The item will display by default on both the parent category's listing and the subcategory's as well. You can also change that behaviour from both the category's settings and the menu item's settings.