It depends on the jurisdiction, as always. Thanks to the LGBA law in the US, you can know exactly who your bank shares your information with. This is an example from Discover, which explicitly says that Discover shares your information “for joint marketing with other financial companies”. I think only Vermont and California residents can limit this kind of sharing.
It could be worse, Discover can legally share your information “with non-affiliates to market to you” but it chooses not to.
PS: I recommend all the US residents looking up “what does [your bank] do with your personal information” and read all of the paper.
Yes but this alternative is only available in Norway and Denmark soon. The opening up of Apple products for alternatives is EU only from what i understand.
The equivalent app in Sweden (Swish) is apparently rolling out similar functionality. The technical details are exceedingly unclear but it remains Android exclusive for now. So far only one bank is on-board, per the article linked, but I expect that to change with time.