I just looked at the gps from my bike ride on New Year's day. The GPS is off by about 30 meters at the start of the route but corrects itself after about 10 minutes. No Internet required. I am surprised it can take 10 minutes for the GPS to get a proper lock. I guess it's a power saving measure.
Yes Navstar GPS and other GNSS constellation satellites have limited power from solar panels and thus the almanac data is transmitted at a low bit rate.
