Most meteorologists gather their data from the same place, the National Weather Service. All they do is basically create pretty charts around it and put on a suit.

Depends on the area and timeframe. If you look areas where there are lots of sensors around - say Europe, forecast for next 2 weeks will be very accurate.

If you are looking at the ocean, where sensors are only placed every 500KM - your accuracy will be very low.

Source: I sail boats and study forecasts occasionally.