My book editor says that we need to professionally reflow the text with Adobe InDesign software (not just in a word processor). She asks $350 what is too much.
Can I do it myself (with Scribus instead of InDesign)?
Do I assume correctly, that after me inserting non-breaking spaces where needed I can just allow the software (Scribus) to do the task? Does this really need a work of a professional editor? Will it be OK if I do it myself with Scribus?
Your book editor is most likely trying to make money on you.
You can look in the wiki to what has been done with Scribus
http://wiki.scribus.net/canvas/Template:TOC_Success_stories
Note however that you will need to learn Scribus first. Scribus may not be as easy to use as a word processor.
One thing you can do is to ask her for the technical requirements. Referring to a specific software (Adobe InDesign) is not technical requirements.