The building has LTE repeaters, micro-cells, and wifi networks. A tight geo is very possible with assisted GPS.
Not really. To geolocate a user the cell providers would need to know the absolute position of all the LTE repeaters and cells (which they might). But they'd also need to compensate for indoor propagation (which is much more complex than outdoor).
Also AGPS only provides satellite ephemeris, which enables a faster time to fix, not better accuracy.
A GPS repeater would only give accurate time, not position. The repeater only repeats the signal that's captured by the antenna on the roof. I use GPS repeaters frequently in my labs to supply timing to instruments.
Extremely questionable. GPS accuracy even outside isn't perfect and GPS accuracy inside is a crap shoot depending on the building. Someone could have been walking past outside and be shown as inside the building.