A lot of the stories of how scientists thought everything would soon be solved are just that... stories. Sort of a variation on the Columbus/flat Geocentric/stupid concepts mentioned before. I've heard it said that it was said but I've never come across writings of a scientist form turn of the century era that said anything of the sort. I'm not sure who/when considered wave/particle duality a trivial thing either.
"Hazy, troublesome, etc" is just what I said it was, General Relativity covers black holes fine, Quantum Mechanics does so less well, as mentioned Quantum Gravity etc present serious concerns and some apparent paradoxes.
Why is Hawking Radiation inversely proportional to the square of mass? I think I called it cube last time, it's lifetime that goes as cube of mass, power is inverse square. It's totally unrelated to gravity except as an ultimate power source for the heat. Anyway, black holes have temperatures, bigger ones are colder. Double a black holes mass and you double its radius, quadruple it surface area, and get 8 times the volume. And skipping some steps, A black hole's temperature is inverse to its own mass. Double Mass, half temperature. You can run through the math on wikipedia, it's mostly algebra.
Well virtually particles don't get blocked the way you're thinking, if they got absorbed by interaction that way then having an object between you and them should mean less gravity then if nothing was in the way which obviously isn't the case.
Gravitons perplex everyone, I wouldn't worry over it much. We don't know if they exert gravity, photons do since electrical fields can, anything containing energy probably does but gravitons may be an exception.
I'm not entirely sure what you're saying.
No, the type of energy is basically irrelevant, but 'heat' is essentially random kinetic energy not potential and that includes photons from blackbody radiation occurring at or under the Universe's temperature. It's the gradual but inevitable conversion of patterned objects into unpatterned ones, or that form which no work can be extracted.
I took roughly 400 years to answer Olber's Paradox, more than half of them passing before it even got named that. One less than a century old isn't one I'm going to elevate to unsolvable, it's not something like
"Is there a God?" or "Is this all a dream?" where one can not conceive of a means of answering the question with certainty and we've not been beating on the problem very long.
- Albert Einstein
King of Cairhien 20-7-2
Chancellor of the Landsraad, Archduke of Is'Mod