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Hi AKhan,
From the requirement provided in your original description, we’re sorry it’s not possible to get the reports for a SharePoint site and there are some activities such as File and page activities in Security & Compliance Center (but it displays all the data of the user for every site). You can refer to this article: Search the audit log in Security & Compliance Center for some detail activities.
For audit log reports provided with SharePoint, you can refer to this article: View audit log reports.
But the ideas you stated are great, we suggest you provide them in SharePoint Online UserVoice for taking this to related team. Your feedback is highly appreciated as it helps to improve functionality of product.
Lastly based on my experience, yes it counts for every time they open the page in browser.
Appreciate your patience and understanding.
Regards,
Chitrahaas