Hi,
Yes you can deactivate the payment and the shipping in order to have just "enquiries".
After that, you can override HikaShop views in order to hide the price for no-logged users or you can use HikaShop Business in order to use the ACL.
It is possible to set ACL on price so, user could access to specific prices depending their group. You can use it for special discount for special users or you can use it as a way to hide prices for non-logged users.
Thanks to ACL, you can configure access in the backend too. So some users could have access to product editing, or orders etc.
If you want more specific rights for non super user access, you can use "HikaMarket Front-end" which allow to manage your products, orders and categories directly from the front-end with a lot of access options.
About your last point, HikaShop have search plugins. One for products and one for categories.
Best regards,