"Motorola" as a brand is now thoroughly axed to death. I can't imagine that the brand will last long on consumer devices when under the Google umbrella, and the enterprise devices are either dying a slow/quick death (3GPP, 3GPP2 being replaced with NSN kit & iDEN cos it's a dying proprietary tech) or being outsourced to another well known brand (TETRA is relying on Ericsson for it's LTE enhancements, IIRC).
So that means that the early GSM patents are just now in public domain
FTFY. The GSM specs have been evolving over the last 20 years, and continue to do so as it enters the last maybe ten or so years of usefulness (and even that's a figure in doubt as the GSM network coverage is so ubiquitous - handset churn rate helps this along, though). GPRS and EDGE and enhancements to the specs, and even UMTS (incl HSPA) and LTE reuse & improve on some aspects of GSM. Patents are still being sought on GSM tech, and the spec still has changes being made by manufacturers and operators - especially when they have a patent on the change proposal
You might possibly be able to make a handset that technically does GSM without infringing on a patent, but it would be rather feature-light (if functioning at all, with modern network infrastructure).
errr - that's not a tardis (hope this isn't a "swoosh" moment, it's a regular old-style public phone box (booth). You don't see them about much, although a while back an enterprising sculptor put a dozen together like this and flogged it to my local council for several tens of thousands of quid.
The tardis is supposed to be a police telephone box, which has a different design and colour like this. These boxes also contained equipment other than a phone - such as a first aid kit and an incident book.
On a last pedantic note, there were red police boxes in Glasgow, Scotland, for a time.
It isn't easy being the parent of a six-year-old. However, it's a pretty small price to pay for having somebody around the house who understands computers.