Hi Piret Daniel,

Yes there are methods to create and edit reports. If you have a look at Power BI REST API, there is one API o create an embed token allowing user to create a new report.

Embed Token - Reports GenerateTokenForCreateInGroup (Power BI Power BI REST APIs)

The API used for embedding an exising report has an access level parameter to control if the report will be available as readonly or read/write. It is called access level.

Embed Token - Reports GenerateTokenInGroup (Power BI Power BI REST APIs)

Power BI team has recently created a playground web site which has lots of samples to show all the possibilities available with embedding.

Power BI Playground