When will Apple remove the methods/APIs marked as deprecated?

In common usage deprecation merely means that the feature is no longer recommended to be used and MAY be removed entirely in a later release.

Wikipedia - Deprecation

It is good practice to stop using deprecated features as soon as it is reasonable to, as you have no guarantee how long they will continue to be supported. Sometimes it could be as little as the next release or many dozens of versions later.

A quick search for Apple and Deprecation brought up this API reference where a feature has been deprecated but has survived at least one major OS revision.

https://developer.apple.com/library/ios/documentation/uikit/reference/UIDevice_Class/DeprecationAppendix/AppendixADeprecatedAPI.html

So yeah, when will Apple remove them? Whenever they want to, so don't build stuff now that relies on them and move old code off of them as you can. The compiler will usually throw warnings when features that are being used have been deprecated.