Does the Android license, being Apache license, permit others to develop their own versions of Android and license them as proprietary? As far as I understand, the Linux kernel on which Android is built is GPL. Then how can Android or further derivatives be released under a different license? What is the sanctity of GPL license of Linux here?
The Android kernel is a variant of the Linux kernel. Since the latter is GPLv2, the former must also be, and it is. So the "sanctity" of the GPL on the Android kernel is intact; you can get the source for those portions at places like this. If you make and distribute your own modified version you will also have source-distribution obligations to honour. However, the licence on the kernel has no effect on what you can run on it: I can run Apache-licensed, GPLv3-licensed, and proprietary software packages in user space on top of my Linux desktop kernel, without offending against the kernel's licence.
The userspace OS is under the Apache licence. This is a weak copyleft licence, and taking the code and making proprietary products from it is lawful, provided you adhere to a few notification-related obligations (remember, IANAL/IANYL).
The applications that run on Android can be under any licence their developers choose.