When adding blocks by clicking the New button on the website, the New button links to the block editing page, which is out of context of page editing. Also you have to add the block to the page (again) when the block has been created.
Click on the New button should open a drop down with the block types
Clicking a block type will open a modal dialog for adding the block
Click on Save should save the new block, close the dialog and add the block to the page
The update should behave like adding an existing block: only the block is updated and the result can be out of context (with multiple content blocks, normally duplicate results are filtered, but not when adding one block because the context is lost)
Click on Cancel should close the dialog without saving
Click on the New button:
Will open a dialog like this (this is a wireframe, not the design):
Test the add block for all block types
Test if the requirements still work when a validation error occurs
Test the cancel for one random block type