Creating Your Own Mobile Application - Based on PHP Web Application

I have developed a PHP application. I want to use phonegap.com or a similar approach to develop my own applications based on the same MySQL database. In other words, connect mobile apps to the web interface.

He must do one or two things differently. First, use your own GPS features to determine where the user is. I assume this can only be done through HTML5?

Secondly, send push notifications every time a web application user receives a notification.

All information is already in the MySQL database, and all but the two functions above function properly.

I currently have an API designed for the entire web application, which makes it API oriented. It will be easy in my head to connect two versions via the API.

For example, a user logs in to a web application. He is then offered the iphone application for download.

Is it possible to get him to log in with the same via iPhone. On the other hand, is it possible for him to search for a database, via iphone and “add a new friend” - to make a connection of two users in the friends table - in this, is a friend also a friend on a web application?

I read a lot about all the options available, and I'm still very confused! Any help would be very helpful.