1. When selecting an image in the Image tab (not the plugin button in the editor) of an article, the File Manager is displayed instead of the Image Manager, this causes problems as the configured file paths are different.

The Image Manager is a dialog available from the editor toolbar, that assists in inserting images with various attributes into an article. The Image Manager and Image Manager Extended have their own parameters for this in the Editor Profiles.

The fields in the Image tab are Joomla fields for the Article Manager, and JCE provides a generic File Browser - with the file type set to display images - to select an image for this field. The parameters for this File Browser can be set in Editor Profiles -> Plugin Parameters -> File Browser. These parameters are used whenever this File Browser is used, including when it is launched from within the Link dialog.

2. Furthermore the File Manager appears to be configured to upload images resizing to 125px, and the thumbnails to 120/90px.
I can't find where to change this.

These parameters can be set in Editor Profiles -> Editor Parameters -> Filesystem.

2. I know that, but something goes wrong, please see the attached screen shots.

Please send me a login - https://www.joomlacontenteditor.net/contact/site-login

Please try JCE Pro 2.7.16 RC4 - https://www.joomlacontenteditor.net/downloads/editor/pro/development

I suppose that it's safe to keep on using this version (2.7.16 RC4)?

Yes, additional bug fixes, if any new bugs are reported, will be added to this version for the release next week.

It's at the top. This forum moves the Accepted Answer beneath the original post.