I went through their API documentation at http://developers.marketo.com/documentation. It would be helpful if Marketo team can help us to identify where to look what.
We need below information from Marketo technical team.
The REST API you will need is call create\update leads: Create/Update Leads » Marketo Developers
Endpoint: Endpoint URL » Marketo Developers
Getting the rest of your fields: You must identify the fields you want returned by the Get Lead by ID API, by default it gives you the fields you mentioned. To get the rest of them you must explicity pass those fields as parameters, please see the documention here: Get Lead by Id » Marketo Developers