I think there should be a hurricane once per real time month. It should start east of the lesser antilles or near the bay of campeche (most starting in atlantic) and loosely follow standard historical tracks.
ships caught in the storm could have a chance of suffering storm damage, even to the point of sinking. however, as with real hurricanes, if you make it to the eye, you find an area of calm.
as for tornadoes - impossible because if you are under sail you would encounter waterspouts, not tornadoes. should hurricanes spawn water spouts? meh - seems like a lot of work programming for little actual return
I recall seeing somewhere there may be 3 day forecasts inserted into the game