The reason you see conflicting information when researching is because these rules are slippery. None of them have a strong backing in science, and their history in aesthetics is less important than in popular myth. There's no evidence whatsoever that anyone used the golden ratio in art before the 20th century, but people have heard the story so many times that they're often unwilling to believe it.

I've written some (detailed, researched, and referenced answers) related to these:

• on the Rule of Thirds
• on the Golden Ratio
• on the Diagonal Method
• and, overall, on Subject Placement According to Rules.

The basic theme is that someone has an idea for a formula for composition, a process which when followed will give scientifically better results without needing to use artistic judgment. Then, a bevy of historical works are analyzed and (through the magic of selection bias) brought out to prove that this technique was the secret of the ancient masters.

Since artistic judgment is a difficult skill, and baffling to many people (to some it comes naturally, but for others only after a great deal of time and effort, and for many people it seems to never "click"), the idea that there's a straightforward solution is very reassuring — like a lifeline dangled into the rough waters of making art.

Having grabbed on to that, it's hard to let go. Of course, many, many people are fine with the idea that the rules are only guidelines, but for others, the structure becomes almost religious, and whole complicated systems get built up around the original rule, both to expand it (like the idea that intersections of rule of thirds lines are "power points") and to relax the restrictions so that more examples comfortably fit (like the idea that a 3:2 aspect ratio is close enough to count as connected to the golden section).

So, to answer the question, the basic answer is: do what works best for the individual image you're constructing. Triangles, squares, and balanced divisions can be useful tools in a composition, but they're your tools, and you should use them in your way. If you find that you're really getting good results with a particular framework, cool! You can make that part of your own style. But you probably shouldn't package that up as a rule for other people — we've got enough of those already.