Welcome to the site, WrittenEmber. You have worded your question masterfully and the topic is quite interesting too! I would love answering it according to my (limited) knowledge.
You have not specified what is the extent of this ash-winter. Has the Earth/planet completely frozen over into a snowball Earth like condition (extreme case) or is it that the layer of ice is only a couple feet thick at most places and the oceans are still liquid? I would assume the second scenario here, as this stage is easier to cure.
1- Would I be right in thinking there might still be life in the oceans?
This is your world. Make it the way you want. If you want that extremophiles living around deep sea vents survive, so be it. If you want everything dead, declare it so. Your world, your rules.
If it were my world, I would have the extremophiles survive in deep sea vents and a few critters surviving on land.
2- So my question is, how quickly could this be expected to happen?
Once sunlight starts reaching the surface, the ice on equatorial regions would start melting soon (as in, within a couple months). Then, as the ice goes on melting in higher and lower latitudes from the equator, it will create a lot of rivers, lakes, flash floods and a lot of topsoil would be eroded away into the bottom of these new rivers, and sometimes be permanently lost into the oceans.
It is only after several years (I would guess 5 years) of the removal of permafrost that the soil would be once again fit for growing plants. Hardy plants at first. Grasses, followed by shrubs and bushes, then small trees and finally wooded regions would appear. From the removal of frost layer to the appearance of first small jungles, it would take nearly 20 years.
Once there is enough food for the grazers (after 10 years of removal of frost layer), you can introduce small animals such as hares, goats, sheep, deer etc. Only after their population is naturally established in an area, you can introduce small predators such as bobcats, snakes and solitary wolves. After the habitats are firmly established (after 20 years of removal of frost layer), you can finally introduce larger animals such as buffaloes, bison, giraffes and zebras, followed by (after 5 years) large predators such as lions, cheetahs and tigers.
One thing you must pay special attention to, is that I have assumed that your nitrogen-fixing bacteria have survived under the frost layer. In case those bacteria are lost, you would first have to introduce those bacteria to the soil, before you plant the first seeds.
3- How soon would the temperatures rise once the sun could reach the surface again?
This depends entirely on the area and its climate. For example, something resembling Africa or South Asia would have its climate return to temperate (notice they are tropical right now, which is warmer than temperate) within around 10 years of the removal of frost layer. As you move up (north) or down (south) from the equator, regions would require longer time frames to return to their pre-frost conditions. For example, England would require at least 20 years to return to normal, after the permafrost is gone. Northern Europe, Canada and northern Russia would require even longer times. Perhaps 30 years or so, before the climate is stabilized. And of course polar regions would remain frozen as before, unless ...
4- How fast would reintroduced plants and animals take hold?
5- How soon could people begin living on the surface, and under what kind of conditions?
People are the hardiest of all mammals. We can live in almost any place, if we have the support of our technology available to us. Even on the permafrost layer, people could live in igloos and in caves.
Normal living conditions (as in, building houses as we know them today) won't start be possible until a very long time, though. That is because we are extremely dependent on the technology for this purpose. You would need wood (at least 25 years after the removal of permafrost layer), cement (only possible after you set up cement manufacturing industries, which would be at least 35 years after the removal of permafrost), metals (only possible after metal refineries are set up, which ... I don't know when would be possible, since you need to know where the ores are located, and also have an already functioning society to have people working in them) and bricks. Thankfully, bricks can be manufactured the earliest of all other ingredients. Nearly 4-5 years after the permafrost layer is removed.
So the initial human colony (the people who came in the spaceship) would be built on the permafrost layer. They would probably live within their spaceship for the most part of their time, only venturing out to see how their technology is helping thaw the world. Once the permafrost layer is gone, they can start building brick furnaces and bake bricks, which would enable them to build primitive homes and cabins. Only after they have wood available and have set up metal refineries, that they would be able to build proper homes as we are used to, today.
6- What might this formerly dark and frozen world plausibly look like after about fifty years of artificial revitalization?
Mostly normal (as in, as it exists today). Although 99.99% of the surface would be natural habitat of plants and animals. The first long-lasting human structures would be starting to be built. These would include metal refineries, housing colonies and small factories.
Animal populations would be very less than modern times, unless the people are continually pumping in more individuals through cloning, every year.
Climate would have been stabilized. Seasons would have returned, although winters would still be somewhat longer than the summers.