The short version before I get a chance to write more posts:

Primates appear to be an interestingly potentiated lineage, prone to getting smart when they get large, due to differences in brain development established 50 megayears ago that make their brains much more impressive per unit volume than most larger mammals. The great apes other than humans actually seem to run into energetic limits to feeding their brains and have smaller brains than you'd expect for a primate of their size, while humans are right on the generic primate trendline. Birds are another potentiated lineage - their brains are about 6x as compact as a comparable primate brain.

Eukaryotes are really weird. The one thing that is incontrovertible these days is that the classic 3-domains-of-life idea, with eukaryotes and archaea as sister clades, is turning out to be wrong. Eukaryotes are turning out to have come from a fusion/symbiosis of a bacterium and something that fits entirely within the archaeal domain. Various people who are studying their origin and evolution have their pet models and hold to them too tightly and fight each other bitterly, though some things are finally coming out for sure. A lot of their weird features may come from particular population genetic selective pressures that come from competition between copies of the mitochondrial genome, and a lot of others may come from the fact that they invented sex and have low population sizes both of which allow types of evolution and genetic drift that you are much less likely to see in the eubacteria or archaebacteria, the two 'primary' domains (whose separation represent the deepest branch in the tree of life). But the fact that ALL eukaryotes have a huge constellation of weird traits with no intermediate forms means their origin was a weird event, and opinions vary on if that means it was a singular extremely unlikely event or if all those weird properties come logically from how they formed, and on if there was strong first-mover-advantage.

And, of course, our data on the breadth of life that exists on Earth is incomplete... I love the specialized journals on electron microscopy, now and then you see a paper where someone just sees something really bizarre and reports on what they saw without a clue as to what it is. If you want a really perplexing paper, take a look at this: http://jmicro.oxfordjournals.org/content/61/6/423.full.pdf+html (alternately https://dl.dropboxusercontent.com/u/67168735/a%20unique%20organism%20from%20the%20deep%20sea.pdf ) "A Unique Microorganism from the Deep Sea"

Now I have!

I think their case is weak but it is something to continue to be considered when analyzing any new data. There's weird soil chemistry there for sure, a good deal of which might be explicable from the interaction between perclorate and small amounts of organics, but the amount of data is tiny and I would not rule out soil microbes. A lot more work has to be done before you can say much with confidence.

I generally have very low confidence in singulatarian ideas of any stripe, 'foom' or non. Partially for sociological analysis-of-the-origin-of-singulatarian-and-related-ideas reasons. Partially for astrobiological reasons relating to the fact that nothing has ever consumed a star system or sent self replicating anythings between stars and my impression of the range of possible outcomes of intelligent living things that are not extinction or controlling the universe and the possible frequencies of things something like us. Partially because I think that many people everywhere misattribute the causes of recent changes to the world and where they are going and have short time horizons. Partially because I am pretty sure that diminishing returns applies to absolutely everything in this world aside from black hole growth.

I can't say I've read Gwern's analysis of computational complexity, but I do note that in the messy complicated poorly-sampled real world you can very very seldom actually KNOW enough to predict much of a lot of types of events with great precision.