I want to write, and sell, a book about a particular piece of software, in particular the open-source community edition.
It would be a how-to/tutorial type book
Do I need the company's permission to write the book?
Can I use the name of the software in the title of the book?
Regarding the vote to close, there are over 1000 questions on this site about licensing. Why do you think it should be closed?
You are best of by contacting them via email and explaining your plan to them and work out something with them. Every company is different so an answer can't really be given.
Yes if you respect fair use of trademarks.
But the most obvious action I expect from you is contacting the authors of the software and explaining your plans.
It's not only polite, but may bring you infos you wouldn't have got otherwise.
As long as you aren't breaking any covenants that you have made with the company, using any information that was supplied to you under and NDA or as part of a contract such as an end-user agreement, they shouldn't be able to prevent you from writing about their software, especially if it is an open-source, community supported package.