Google Analytics: how to tie together web, chrome extension and backend analytics?

Background: I have built a website & extension. It's a basic video transcoding service. A user installs the chrome extension on chrome store or by clicking a link on my website. Then, they install and use the extension to define videos on the page they are viewing. To convert the videos they defined, they must login on the website, and run the jobs. The server converts the videos and provides information about whether they were successful or not and other information.

Goal: Using google analytics, I want to track the number extension installs, extension events (how the user is using the extension), membership sign-ups and also number of logins. When they submit jobs using the extension, I want to also record the result of those jobs from the backend. How can I achieve this massive feat, tying together analytics from the web, chrome extension and the backend?

To make things worse, I found two conflicting documentation, not sure which one I should be using. One is using ga() and the other _gaq.push()

This documentation on chrome extension analytics redirects me to another page -- which looks very different than the one I was reading.

My end goal is to build a flow graph that will tell me a completely story of:

• Where the visitors are coming from
• How many of them install the extension
• How many people sign-up and login
• How people use the extension to submit jobs on the server, record successful jobs vs failed jobs

I would also like to know how many people end up paying for the service.