First question: One thing that children can aquire earlier which might help them with musicality is relative pitch (or they can even sustain absolute pitch). There is a study which shows that babys can remember music played to them before their birth, to the degree that they can even recognise changed notes afterwards (
https://journals.plos.org/plosone/artic ... ne.0078946).
As a fun fact on the side: The "skill level: asian"-meme has actually some basis in the real world when it comes to relative/absolute pitch (and maybe therfore musicality?). Studies show that speakers of tone languages (such as Mandarin, Cantonese, and Vietnamese) possess absolute pitch to a much high degree (
http://deutsch.ucsd.edu/psychology/pages.php?i=215). Another side note: With learning an instrument at a young age there is also less risk of your kid choking to death.
Back to seriousness: Go has an aweful feedback loop which makes learning it harder than learning an instrument. Assuming that you're less tone-deaf than I am, you will hear yourself play a note wrong - instantly. On the other hand look at DDK-games. With 30 minutes main time each. And nobody knows what anybody did wrong besides those captured stones on move 250 because one player missed a liberty shortage.
Another important learning technique is compartmentalisation. You focus your practice on specific parts of the skill instead of doing everything at once. Musicians will practice the difficult part of a piece over and over again. Musicians will go through scales over and over again to build up "muscle memory". How to achieve that in go? Solving locally isolated situations is nice but just compared to the stuff musicians do it is highly inefficient. When you practice scales or a difficult part you still hear your perfomance, it still has to sound right. You are - in a sense - still connected to everything your instrument and music is. Solving locally isolated situations has much less to do with playing a real go game. With the whole board to play on, killing a group or getting a ko might be the wrong move. As might be living in gote (or living at all). Don't get me started on opening patterns with a "locally even result" or calculating fractions in the endgame.
To go on another short tangent: Nowadays I believe that - after you got your first hunch of the basics at around strong SDK - the best way to efficently study go is to go over professional games. A lot of them. Constantly. Make your unconsciousness work for you and remember that pro players don't necessarily read deeper than you, they just choose better starting moves and don't read obvious bad sequences ; )
Just to make it clear: Solving locally isolated situations will make you a better go player over time. But investing the same time in learning an instrument yields a higher ROI in my opinion.
Second question: No input.
Third question: Teaching has most certainly evolved for the better. Well, ...let's say there are now much better teaching methods available because there is more knowledge into the science stuff behind it. Whether or not you or your teacher follow those methods is another question.