Thanks for your insight.
I think if you looked thoroughly throughout the settings and our documentation, you'd find this is mostly all present, already, though without the specificity for iPhone or iPad. However, we do provide the Browser Specific CSS plugin, free in our store that lets you create your own customizations for the iOS system. We cannot provide settings for every mobile OS as there are many more than you think, and often subject to change by their developers.
For the Apple image (iOS icon) just go to Dashboard > PageLines > Site Options > Website Setup and scroll down. It's called "Mobile Touch Image".
PageLines, by default, creates a mobile template to avoid people excessively customizing or making incorrect template customizations for mobile view. Essentially, it picks up the layout of the template assigned to the page, but manages things like sidebars in ways to prevent making your site's mobile view very small. You can always create a custom template: http://support.pagel...-page-template/
I'm unsure about Retina, but do believe someone's created a plugin or section for that in our Store.
The grid already exists. http://demo.pagelines.me/tools/
You'll find that our documentation helps considerably in answering many of your issues.