Amoeba Updated +Created
This group is a mess.
But one thing you should really know, as often mentioned in Power, Sex, Suicide by Nick Lane (2006): they are all eukaryotes.
Because prokaryotes are fundamentally unable to do phagocytosis, because they have a rigid cell wall. Changing cell shape at will requires a cytoskeleton.
Apoptosis Updated +Created
Power, Sex, Suicide by Nick Lane (2006) part 5 "Murder or suicide" mentions that apoptosis has two main functions:
Apoptosis is largely regulated by mitochondria Updated +Created
Power, Sex, Suicide by Nick Lane (2006) part 5 "Murder or suicide" mentions that the key events that leads to apoptosis is when certain proteints normally present in the inner mitochondrial membrane spill out, and that this often happens when free radicals are produced in excess: the cell is really not doing well in those cases. This point suggests that the initial mitochondrial endosymbiosis happened due to a parasite that lived inside another cell. It mentions that even today we see parasites kill the host cell when they feel that the cell does not have many nutrients. This frees the parasites to then infect other cells.
Archaea are more cosely related to the eukaryotes than bacteria Updated +Created
ATP synthase Updated +Created
One of the most beautiful molecular machines known!
The first one with such complexity that was uncovered.
The thing rotates like a water wheel for God's sake, except it uses protons instead of water.
The ATP synthase complex is so large that Power, Sex, Suicide by Nick Lane (2006) page 123 contains a cryoEM image of several ATP synthases on small membrane vesicles, this is the paper: pubs.acs.org/doi/abs/10.1021/bi00437a031# under a fucking paywall.
Video 1.
ATP synthase in action by HarvardX (2017)
Source.
Cancer is natural selection gone wrong Updated +Created
A cool thought about cancer expressed at Power, Sex, Suicide by Nick Lane (2006) is that cancer it is the direct product of natural selection gone wrong!
Cancer cells are obviously selected against anti-cancer mechanism, which when they manage to evade, they reproduce uncontrollably, gaining more and more momentum.
Eukaryotes can do phatocytosis due to their cytoskeleton Updated +Created
Power, Sex, Suicide by Nick Lane (2006) page 53 suggests that one tremendous advantage of eukaryotes over bacteria is their ability to change shape due to the presence of the cytoskeleton, and the lack of a rigid bacterial cell wall.
Imagine in a world where there are only bacteria, and you can eat entire bacteria in one go, what a huge advantage that is!
Because DNA replication is a key limiting factor of bacterial replication time, such organisms are therefore strongly incentivized to have very minimal DNAs.
Power, Sex, Suicide by Nick Lane (2006) 7 "Why bacteria are simple" page 169 puts this nicely:
Bacteria replicate at colossal speed. [...] In two days, the mass of exponentially doubling E. coli would be 2664 times larger than the mass of the Earth.
Luckily this does not happen, and the reason is that bacteria are normally half starved. They swiftly consume all available food, whereupon their growth is limited once again by the lack of nutrients. Most bacteria spend most of their lives in stasis, waiting for a meal. Nonetheless, the speed at which bacteria do mobilize themselves to replicate upon feeding illustrates the overwhelming strength of the selection pressures at work.
Key mitochondrial proteins aren't necessarily in mtDNA Updated +Created
E.g. in humans the adenine nucleotide translocator is present in chromosome 4, not in mtDNA.
These have almost certainly been transferred to nuclear DNA in the course of evolution.
This isn't completely surprising, since when mitochondria die, their DNA is kind of left in the cell, so it is not hard to imagine how genes end up getting uptaken by the nucleus. This is suggested at Power, Sex, Suicide by Nick Lane (2006) page 196.
A limiting factor appears to be that you can't just past those genes in the nucleus, further mutations are necessary for mitochondrial protein import to work, apparenty some kind of tagging with extra amino acids.
However, you likely don't want to remove all genes from the mitochondria because mitochondria have DNA because they need to be controlled individually.
Mitochondria have DNA because they need to be controlled individually Updated +Created
Basically, energy supply has to be modulated rather quickly, because we spend a lot sometimes, and very little other times.
Even not turning it off quickly enough is a problem, as it starts to generate free radicals which fuck you up.
If control came from the nucleus, it has no way to address different mitochondria. But it might be that only one of the mitochondria needs the change. If the nucleus tells all mitochondria to stop producing when only one is full, the others are going to say: "nope, I'm not full, continue producing!" and the one that need to stop will have its signal overriden by the others.
Mitochondrial DNA mutates faster than nuclear DNA Updated +Created
Wikipedia mentions "Since animal mtDNA evolves faster than nuclear genetic markers" with a few sources.
Some sources:
Mitochondrial protein import Updated +Created
The process that imports proteins encoded in the nuclear DNA and made in the cytosol into the mitochondria.
The term is mentioned e.g. in this article: www.nature.com/articles/nrm2959.
Power, Sex, Suicide by Nick Lane (2006) suggests that proteins are somehow tagged with extra amino acids for this.
Mycoplasma genitalium Updated +Created
Size: 300 x 600 nm
Has one of the smallest genomes known, and JCVI made a minimized strain with 473 genes: JCVI-syn3.0.
The reason why genitalium has such a small genome is that parasites tend to have smaller DNAs. So it must be highlighted that genitalium can only survive in highly enriched environments, it can't even make its own amino acids, which it normally obtains fromthe host cells! And because it cannot do cellular respiration, it very likely replicates slower than say E. Coli. It's easy to be small in such scenarios!
Power, Sex, Suicide by Nick Lane (2006) section "How to lose the cell wall without dying" page 184 has some related mentions puts it well very:
One group, the Mycoplasma, comprises mostly parasites, many of which live inside other cells. Mycoplasma cells are tiny, with very small genomes. M. genitalium, discovered in 1981, has the smallest known genome of any bacterial cell, encoding fewer than  genes. Despite its simplicity, it ranks among the most common of sexually transmitted diseases, producing symptoms similar to Chlamydia infection. It is so small (less than a third of a micron in diameter, or an order of magnitude smaller than most bacteria) that it must normally be viewed under the electron microscope; and difficulties culturing it meant its significance was not appreciated until the important advances in gene sequencing in the early 1990s. Like Rickettsia, Mycoplasma have lost virtually all the genes required for making nucleotides, amino acids, and so forth. Unlike Rickettsia, however, Mycoplasma have also lost all the genes for oxygen respiration, or indeed any other form of membrane respiration: they have no cytochromes, and so must rely on fermentation for energy.
Downsides mentioned at youtu.be/PSDd3oHj548?t=293:
  • too small to see on light microscope
  • difficult to genetically manipulate. TODO why?
  • less literature than E. Coli.
Data:
Parasites tend to have smaller DNAs Updated +Created
If you live in the relatively food abundant environment of another cell, then you don't have to be able to digest every single food source in existence, of defend against a wide range of predators.
So because DNA replication is a key limiting factor of bacterial replication time, you just reduce your genome to a minimum.
And likely you also want to be as small as possible to evade the host's immune system.
Power, Sex, Suicide by Nick Lane (2006) section "Gene loss as an evolutionary trajectory" puts it well:
One of the most extreme examples of gene loss is Rickettsia prowazekii, the cause of typhus. [...] Over evolutionary time Rickettsia has lost most of its genes, and now has a mere  protein-coding genes left. [...] Rickettsia is a tiny bacterium, almost as small as a virus, which lives as a parasite inside other cells. It is so well adapted to this lifestyle that it can no longer survive outside its host cells. [...] It was able to lose most of its genes in this way simply because they were not needed: life inside other cells, if you can survive there at all, is a spoonfed existence.
and also section "How to lose the cell wall without dying" page 184 has some related mentions:
While many types of bacteria do lose their cell wall during parts of their life cycle only two groups of prokaryotes have succeeded in losing their cell walls permanently, yet lived to tell the tale. It's interesting to consider the extenuating circumstances that permitted them to do so.
[...]
One group, the Mycoplasma, comprises mostly parasites, many of which live inside other cells. Mycoplasma cells are tiny, with very small genomes. M. genitalium, discovered in 1981, has the smallest known genome of any bacterial cell, encoding fewer than 500 genes. M. genitalium, discovered in 1981, has the smallest known genome of any bacterial cell, encoding fewer than 500 genes. [...] Like Rickettsia, Mycoplasma have lost virtually all the genes required for making nucleotides, amino acids, and so forth.
There are no known eukaryotes which never had mitochondria Updated +Created
As of 2020, there are no known eukaryotes which have never had mitochondria.
Known eukaryotes without mitochondria, which are very rare, have lost mitochondria they previously had.
Having mitochondria appears to be a requisite for being an eukaryote. This is one of the central thesis of Power, Sex, Suicide by Nick Lane (2006).