yes, the Siri AI is actually running on Apple servers if you want to use that service of it. but Apple is not data mining that info like Google does. it's not compiling and profiling you into a whole data base "all about you" from it and other Apple apps to sell ads/services like Google does - you're anonymous on that side of the connection. and don't pretend there is an equivalency of some kind. there just isn't.
Apple has other ways of selling targeted ad space. For example, they use our personal info and preferences gathered from iTunes, plus our location.
That's not my experience. Can you give an example of what you mean?
On Android, you can turn off personalized search results, location history, etc. That does not stop search from working. You can do the same for the web as well, via your Google Dashboard.
Obviously if you signed out of your Google account, then things like Mail and Notes would not work, but if you wiped out Siri's access to Contacts, you'd be in the similar situation of not being able to say "Siri, call Mom".