There are a lot of very open-ended questions which are best teased out into separate thread (topics) to explore in depth - I'm not clear if you're asking whether tto do these things or the mechanics of how to do them. Anyway, Mark B has answered the one/many document question. In ssence it boils down to the breadth of your data and personal choice. Get the split wrong? It doesn't really matter. Splitting or merging Tinderbox documents is possible so if in doubt it's better to just dive in rather than get stuck in analysis paralysis and not get started.
Quote:–make notes with my own summaries and observations, linked to appropriate quotes as needed (I understand that this can be done as well)
You can make notes and and link them to references to books (or store the reference in the note), or make notes representing books you're studying and link your commentary notes that. The 'right' way will again on your style and needs. Visually-focused people will tend to Maps as a primary view, others prefer Outline or Chart view. The context (app view type) in which you do your main review and analysis will colour how you will want to customise your file. If you use Bookends (BE) as your database for citations, Tinderbox (TB) supports drag-drop of BE reference data.
Quote:–be able to sort my book list by topic, author, etc.
All TB containers (notes containing other notes) and agents can sort their contents on pretty much any system attribute and any user attorbutes (the latter being those you add to your TB document). The simplest way is via a container's (or agent's)
Rename dialog.
Quote:–sort notes and quotes from different books by topic, be able to both make connections between ideas from different books by hand (with links or whatever) and serendipitously discover connections through some kind of intelligent search mechanism.
To sort by something like 'topic' you will need to decide how this is indicated. It might be a word of phrase in existing note text ($Text attribute) or it might be values you have placed in a user-created attribute. For instance you might add an attribute $Topic that you could populate and then search via agents. In making such an attribute, consider whether it will only hold one topic per note or several; for the former a String-type attribute is got whereas for the latter a Set-type attribute would be a better choice.
Quote:–store blog posts/essays and ideas for new blog posts, sorted by topic so I can see at a glance what topic I haven't written about in a while, with links to book notes or other relevant articles or websites as needed
Sorting has already been covered - but if you want help with the mechanic of sorting do post a question in the Q&A forum
Tip: you'll find you get more/better answers by separating questions into more tightly defined threads. Posting a number of different questions in separate threads is actually a help to everyone - more posts are good - as topics can be dealt with in more detail.
Do keep the questions coming, and don't be wary of just diving into Tinderbox use - unlike many applications it doesn't penalise for not making 'correct' guesses about use as you start out. Indeed, one of it's strengths is allowing you add any necessary structure as its need becomes apparent.