Can Mindmanager create a "map part" having some connected topics for concept map usage?

Unfortunately I don't think this is possible. Topics in concept maps are really floating topics with specific formatting. They are linked to other concept topics not in a conventional mind map tree but with specially-formatted relationship lines. Therefore Map Parts treats a group of related concept topics as unconnected floating topics.

Also, I was unable to get map parts of any sort to insert as a new topic in a concept map.

Alex, many thanks for the reply!
I was so excited about the possibilities to explore "concept maps" in MindManager, but to develop it in a practical context is getting very frustrating. Using CmapTools or VUE is so pleasant. I can't understand why MindManager advertises "concept maps" support, but delivery such a bad workflow and tools for handling that!

I've had a quick look at Cmaptools and VUE and they both appear to have been built from scratch as concept mappers.

On the other hand, MindManager was designed to create tree-based mind maps and still retains that fundamental paradigm. Its abilities have been expanded to provide basic concept mapping support but this is not its primary role, in much the same way that PowerPoint provides basic graphics capabilities but is not a fully-fledged graphics program. In both cases if you mainly want to create concept maps or to create complex graphics you are better off obtaining the appropriate specialist software.

Having said that however, it is likely that MindManager's concept mapping and graphics capabilities will improve in future versions. Corel, MindManager's new owner, has a strong background in graphics software and has already started to develop MindManager's capabilities in this area.