I do not think this is a complete answer, but I saw an opportunity to grind some of the rust off of my chemistry skills and give us a starting point for the "how much complexity could life on a rogue planet have" portion of your question.
As this is an estimate of available chemical energy from hydrothermal vent fields on a planetary scale, these numbers should be viewed as very, very rough estimates. It's also worth noting I haven't been a professional chemist for around four or five years at this point, and I studied biochemistry and genetics to boot. If a real organic chemist wants to wade in and prove me wrong, I'll gladly step aside and eat my notes.
With that out of the way: the chemistry.
In the basic chemosynthetic reaction as given on Wikipedia (yes, you may wince), hydrogen sulfide is converted to glucose by the following equation:
18 H2S + 6 CO2 + 3 O2 --> C6H12O6 + 12 H2O + 18 S
My approach was:
- Calculate the net energy from this reaction
- Find the average amount of sulfur emitted by a black smoker
- Find an estimated number of hydrothermal vent fields on the planet
I did have to do a little leg work at each stage. Here goes.
Calculate Net Energy
Bond enthalpy of the reactants:
(energy present in the chemical bonds on the left side of the above chemical equation)
H2S: 679 kJ/mol * 18 = 12,222 kJ/mol
CO2: 803 kJ/mol * 6 = 4,818 kJ/mol
O2: 498 kJ/mol * 3 = 1,494 kJ/mol
Total chemical bond enthalpy (reactants): 18,534 kJ/mol
Bond enthalpy of the products:
(everything on the right-hand side of the equation)
C6H12O6: 9,546 kJ/mol
H2O: 459 kJ/mol * 12 = 5,508 kJ/mol
S: 226 kJ/mol * 18 = 4,068 kJ/mol
Total chemical bond enthalpy (products): 19,122 kJ/mol
A note on the carbohydrate - I used glucose, as it is generally the most common simple sugar used as a chemical energy store/source, but there are a few sugars with the empirical formula C6H12O6. This whole thing is an exercise in approximation though, so I'll continue to muddle along.
reactant enthalpy - product enthalpy:
18,534 kJ/mol - 19,122 kJ/mol = -588 kJ/mol
This represents roughly the net energy stored by a chemosynthetic organism using this process. These numbers will vary based on many factors, particularly catalyst presence and material phase - the values I am using here assume everything is a gas, as that is the simplest case for most reactions.
However, I want to analyze this from the perspective of hydrogen sulfide, H2S. We have 18 moles of that present in this reaction, so I need to divide by 18 to get the per-mole energy.
-588 kJ/mol / 18 = -33 kJ/mol
Great. Now we need to know how much hydrogen sulfide is entering being launched into the world's oceans.
Globally Available Hydrothermal Hydrogen Sulfide
Energy per Smoker
According to "Evolution of the Global Biogeochemical Sulphur Cycle" (linked above), the average amount of hydrogen sulfide emitted by a black smoker is approximately 6 tonnes per year.
Hydrogen sulfide has a molar weight of 41.1 g/mol, so 6 tonnes divided by 41.1 g/mol gives us 145,985 moles of H2S being produced per year.
Combining this with our previous value of net energy per mole gives us the available energy per smoker.
33 kJ/mol * 145,985 moles = -4,768,856 kJ of energy per smoker per year, assuming our chemosynthetic life is capturing 100% of all available hydrogen sulfide.
Number of Smokers
Our second paper, "How many vent fields? New estimates of vent field populations on ocean ridges from precise mapping of hydrothermal discharge locations" surveyed approximately 15,000 km of undersea ridge, or about 20% of global undersea ridges (their estimation).
15,000 km / 0.2 gives us an estimated total undersea ridge length of 75,000 km.
This paper also mentions finding plumes separated by 19 +/- 25 km. Using the widest average separation of 44 km (19+25) to be conservative, we can calculate the estimated number of active smokers:
75,000 km / 44 km = 1704 active smokers
Next, we combine this estimate of of active smokers with the moles of hydrogen sulfide produced by one smoker:
145,985 moles * 1704 active smokers = 8,126,131,387 kJ of energy from hydrogen sulfide annually, across the globe. Dropping some digits, that's 8.13 TJ of power.
That's a pretty big number, and life can certainly, ah, find a way with it, but when compared to solar energy it seems much more modest - according to Wikipedia again, the solar energy Earth receives is roughly 3.8 YJ per year. That is nine orders of magnitude greater, which makes our oceanic H2S energy budget a rounding error.
So we have a total global energy budget. What can live off of this?
At the bottom of the food chain, lots of things. That's a whole lot of energy for simple organisms who live off of unusual chemistry and thermal energy. If you wanted a plant-analog which coats these areas, that is not completely outside of the realm of possibility. They'd want to spread via some sort of spore or perhaps jellyfish-like seed or larvae however, as the warm water vents responsible for most sulfur output that's easy to get (not TOO hot) tend to gradually open, collapse, get blocked, or otherwise move around fairly routinely.
For motile multicellular life, we have to move up a trophic level. That means about a 10x loss in available energy. I'll use Blue Whales as a reference and say our leviathan is only about two trophic levels up (Blue Whale eat various small critters which eat photosynthetic life, so, maybe oversimplifying, two steps), which gives us at most 1/100th the available energy.
0.01 * 8,126,131,387 kJ = 81,261,313 kJ, or 81 GJ.
One Blue Whale needs about 400,000 calories per day, which a Google Calculator conversion tells me is 1.7*10^9 joules, or 1.7 GJ.
So, our total energy budget from hydrogen sulfide could in theory support 47 of our Blue Whale-like leviathans (81 / 1.7), if they were very good at sharing. The geneticist in me has some issues with that number in the long run.
It is worth noting that this is only one source of chemical energy, and likely represents only a portion of the total energy available - I haven't touched silicates, ferric compounds, or any number of others. Hydrogen sulfide was simply the lowest-hanging fruit to me, and hopefully this gives you a good starting point for estimating the likely limits of the life on your world.
I'll also give Alexander a shoutout for their comment on evolutionary time - it would indeed take millenia for chemosynthetic life to adapt to another food source, diversify, and proliferate in the newly-found sunlight.