I think maybe we use different definitions of “rote learning”! You say “rote learning might work, especially in combination with understanding the etymology and stroke composition of a character”, but I would argue that that isn’t rote learning any more. 🙂 Merriam Webster defines “rote” as “the use of memory usually with little intelligence: learn by rote”. So I agree with you, rote learning works if you add understanding to it. 🙂

The other questions are a bit trickier. Written colloquial Cantonese is definitely not mutually comprehensible with written Mandarin, although it’s sometimes possible to guess what some things mean. The reason people say that is because people who speak Cantonese write in Mandarin. This question on SE Chinese might help clarify things for you. When it comes to simplified and traditional Chinese, you can check this article, which gives a very in-depth answer to the question of which is easier. As to your last question, learning to read the other set is very easy. Learning to use it actively in handwriting is harder, but not anywhere near as hard as learning to write in the first place.

I’d also like to make a point about traditional vs simplified. It seems like traditional characters are easier to memorise mnemonically, whereas simplified are stripped of many useful clues.

I have a question. I read on https://pandaspeakschinese.com/chinese-names-general-information that Mandarin and Cantonese speakers enjoy 100% intelligibility in writing. Does that also mean that people from mainland China can easily read traditional and vice versa?

拨 and 拔 tripped me up recently as they look similar, have a similar pronunciation, and both involve an action with the hand. Of course this probably isn’t an issue in traditional writing, as 拨 is 撥. I don’t really have a great solution at this time, other than 拨 has the 发 component and so one meaning of 拨 (to allocate, set aside, or distribute, as in 拨款) is a bit similar to some meanings of 发.