Science and physics once said fusion and fision were impossible
Alchemists spent most of early human history trying to change elements into other ones. The concept of the nucleus was discovered at roughly the same time as the discovery that it can change (aka, radioactive decay) - around the end of the 19th century - which immediately launched searches into the possibilities of various means of transmutation. There was no point in time in which the nucleus (aka, a fundamental requirement for either fusion or fission) was known where there was any sort of acceptance that it could not be changed. There was a period of about 75 years where the nucleus was unknown, but the concept of atoms was known. However, fission and fusion wouldn't have made much sense as concepts without the concept of a nucleus.
the sun couldn't possibly exist as it produced more energy than physically possible.
Nobody every believed "the sun couldn't possibly exist". There was a period before the discovery of fusion where there were disputes between geologists and astronomers, with the former believing that the world was older and the latter believing that it was younger (they knew that stars could be powered by collapse - and indeed, they are during their formation - but not of a continued power source). This was a well known dispute and was treated as an unsolved problem, not a "gee, we were all wrong" thing.
couldn't explain how the honeybee flew
There was never any sort of mystery among scientists about how honeybees flew. People can't even track down the origin of this widely cited myth precisely, although there's a number of different theories crediting it to different individuals. A likely source is from a French entomologist, Antoine Magnan, citing secondhand off-the-cuff calculations from an assistant (and had nothing to do specifically with bumblebees). There was never any sort of "scholarly mystery" debated among mystified scientists about impossible-flying bumblebees.
or heavier than air travel.
You're citing Lord Kelvin, but he also had a lot of crazy ideas about things being impossible, even things that had already been invented. During Lord Kelvin's day, there were many respectable teams working on heavier than air aircraft. Not to mention that nature had already more than demonstrated that it was possible, given a sufficient power to weight ratio.
We already have working theories on bendIng space.
Yes, if you can make a continuous chain of black holes along the entire path, for example. Gravity bends space. Inflation bends it in the other direction. We know of nothing else that bends space, and have good evidence that nothing else does.