Conjecture, omen, prophecy, augury...
An augury is a divination based on the appearance and behaviour of animals, or, by extension, any omen or prediction.
If you mean "prediction gov", it is the official government weather prediction website.
Sure, a synonym for "auspices" could be "patronage" or "support."
good or bad
an omen or prophecy
No, an omen is a sign, which can mean good, bad, dangerous, etc. And a warning is something that is going to happen. For example the clouds are dark grey, that is a warning that a storm is coming. A omen is something religious and can be and mean different things to different people.
It is a bad omen
to blurtit out
Good luck
the foretelling or prediction of what is to come.
A prediction is the strong belief that something will happen. It is said to be a true prediction if the event happens. Before the event takes place, you would have to ask the prophet/psychic making the prediction what it means. After the event, or after the prediction is proven false, you can see for yourself what it means.