Karlie here from the Shopify Support Team! Good question! There is a report in the Shopify Analytics section of your Shopify Admin that would allow you to see some customer behaviours, like most searched items and sessions by device or landing page. If you're interested in checking out the Behaviours report from your Shopify Admin, then you can check out our handy help guide, here.
I understand that the Behaviour support doesn't offer as much information as you're looking for, so you could look into using an integrated app with Shopify. I would recommend checking out a couple of apps that would help you create custom reports, so that you can see different statics - like page views. Be sure to check out the apps; PageView and Advanced Reports.
Another option would be to use Google Analytics. Google Analytics is a great way to find statistics for your store. You can read more about Google Analytics and Shopify, here, if you're interested. With Google Analytics, you can actually set up goals and funnels so that you can keep track of certain customer actions from within your store. We have a detailed guide about how to set up funnels and goals, here. If you're wanting to use Google Analytics from within your Shopify Admin, then you could always look into the app; Analytics Buddy as well - this app basically provides all of your Google Analytics data in a dashboard form within your Shopify Admin> Apps section.
I hope this has answered your question. If not, or if you have any further questions please let me know. I will be happy to help!