Hello! Unfortunately, I'm not knowledgeable enough about the Taino to give you a breakdown myself, however, I am familiar enough with the literature to point you in the right direction.

You should know up front that scholarship on the Taino tends to be written in a dry way and premised on the reader's understanding of basic archeology and anthropology, so if you don't have that background certain sections may be slogs.

The classic text on the Taino is The Tainos: Rise and Decline of the People Who Greeted Columbus by Irving Rouse, which is still available on places like Amazon. It served as a reference point for decades of scholarship, so it might not be a bad place to read up.

However, it has two major flaws as far as what you're looking for. 1) Important sections are based on theories which are now out of date and 2) It really does not get into their religious systems too deeply.

A more recent work by one of the most preeminent scholars in the field right now is Taíno Indian Myth and Practice: The Arrival of the Stranger King by William F. Keegan. I recommend this with the caveat that while I've read other works by Keegan and know through other scholars in the field that he is very respected, I have not read this book in particular.

I have read The Caribbean before Columbus by William F. Keegan and co-author Corinne L. Hofman, however. It's a really good summary of a lot of problems related to scholarship on pre-Columbian civilizations in the region. It also directly addresses the problems with Rouse's theories. Certain sections are... We'll call them 'less than accessible', but those tend to be the sections where they get into the nitty gritty of X or Y dig site. The sections where they talk about the period in broadstrokes were pretty accessible and well written, in my view. Certainly more than Rouse.

You're also welcome to check out work by your fellow Boriqua, Antonio Curet, who was kind enough to come onto the AskHistorians podcast with me earlier this year. You can listen to the episode here. The episode does not get too far into the details of Taino religious beliefs, but is a good (accessible) overview of the state of scholarship right now.

An important point which Keegan and Curet make, but which you might not be aware of, is the problem with 'Taino' as a category.

The main issue is that it is very unclear who, if anyone, identified as Taino. Taino is a term used by scholars to refer to a large group of peoples with varying traditions and linguistic traditions, not to mention group identities. It is not how the Taino referred to themselves.

Older scholarship held the view that the Taino arrived a relatively short time before Columbus' expedition. More recent scholarship points to them having arrived in the Greater Antilles at least centuries earlier, if not more. While their languages appear to have all derived from South American Arawak dialects, by the time Columbus arrived these groups spread across the Greater Antilles likely had developed their languages even further. Kind of like Romance languages as they relate to Latin. You might understand some words, but it wasn't the same language.

It is unclear if there even exists a term used by the Taino to refer to themselves as a group and to differentiate out-group peoples such as the Guanahatabeyes of Western Cuba, who were likely migrants from what is today Southern Florida.

Hope this helps.