Science is about provability, consensus is about getting majority or even a plurality of opinions.
I'm afraid not. Mathematics is about provabiity. Science is about predictability (or understanding). That's why science must be repeatable.
These two things are mutually exclusive.
Again, I'm afraid not. You inevitably need a consensus that something has been "proven". You need independent verification that your results are correct and if no one can reproduce your results, they won't be accepted and won't be considered "proven".
Piltdown Man was once "consensus". We know how that turned out.
As early as 1913, David Waterston of King's College London published in Nature his conclusion that the sample consisted of an ape mandible and human skull. Likewise, French paleontologist Marcellin Boule concluded the same thing in 1915. A third opinion from American zoologist Gerrit Smith Miller concluded Piltdown's jaw came from a fossil ape. In 1923, Franz Weidenreich examined the remains and correctly reported that they consisted of a modern human cranium and an orangutan jaw with filed-down teeth.
- Piltdown Man page on Wikipedia
I'm not too familiar with the case, but I'm doubtful that there was ever a consensus on his piltdown man, even among the people that didn't want to believe that Dawson was a con man, there was much disagreement over how the fake find should be interpreted.