The Beats brand was a great entrée to an entire market segment that Apple was trying to better access. I'd say it was a masterful acquisition (and integration).
Yep! I own both a pair of AirPods and a pair of Beats. The Beats were designed for a lower price point, without noise cancellation, than the AirPods so I can’t offer a head-head comparison.
Beats brand basically disappeared after that or at the least has become "uncool".
Apple had iTunes already, they very well could've acqui-hired and improved their service themselves.
Apple music slowly died and is only becoming resurgent now, many years later.