Problem with powering ublox NEO-6M GPS module
The module may very well be dead now, due to giving it 5V.


But depending on which board the module is mounted on, there might be a voltage regulator that expects 5V. Check the specifications for the board you bought.


A window means that at least 50% of the sky is blocked by the building. The module might not be able to get a signal from enough satellites for a cold start.
A voltage divider only works if there is constant current. As you've noted, you just created an unstable power supply.
The datasheet says 27 s but that is probably with a clear view of the sky.
Next to the 5V pin on the Uno is a 3.3V pin. How about using that?
Visually, no. But the Arduino should be able to communicate with the module if the module still works, regardless if the module has a GPS fix or not.