From the offical documentation, I think there are two ways to access Salesforce data from a hybrid app:
a. REST API
b. download a Visualforce page which connects to a Apex controller to query data
(Please correct me if my understanding is invalid.)

As we do not want to consume vast amout of API calls, we are trying to access the Salesforce data through a VIsualforce page. However, there are no specific documentation to walkthrough the ways to 'embed' a Visualforce page into a hybrid app. We tried to directly open the page (.../apex/page) through an in-app browser but sometimes this requires extra login despite the fact that the login process is completed when the app starts.

Anyone knows the correct way to open a Visualforce page inside a hybrid app?