Are there specific organizational processes or tools (not necessarily software) that can help in developing and structuring research ideas?
May I recommend Org mode? It's free software, and it was created by Carsten Dominik, an academic himself. Its focus is to help you maintain hierarchical notes and to-do lists, but it has a lot of other features that are useful for juggling large amounts of information, such as tags, links, many kinds of summary reports, and capture (a way to quickly add a note in the right place before you forget it), as well as many features useful for scientists in particular, like tables, spreadsheets, mathematical notation, export (as papers, slideshows, or websites), and support for source code and reproducible research. Perhaps best of all, Org documents are text files, so you can munge them with standard Unix tools at whim. I've moved more and more of my workflow to Org since I started using it in 2010, and I regret nothing.

Org has a steep learning curve, which gets steeper if you aren't already a disciple of the Church of Emacs. But as I see it, getting used to Emacs is worth it even without Org mode, especially if you do a lot of programming. I was an Emacs zealot for years before I took up Org.