Hi,
A search feature could complexify the structure of the website but it would still be possible with just categories and using HikaShop filters instead of the Joomla search.
The cart would also be shared through all the website in that case.
But even then, you could easily have the carts and the search separated using JMS multisite in order to have virtual websites on your website:
www.jms2win.com/
That way, you would effectively be able to separate anything on your website.
So there are solutions, which can be more or less easy, it depends how far you want to go.