Capillaries are one cell thick and so this makes them very thin. capillaries are also arranged in networks known as capillary beds, and thus multiple capillaries are spread over a large area.
It would have to be an animal cell becuase it doesnt have a cell wall and has a flagella.
I believe the process of fossilization still occurs today. The reason being why we find fossils is because of the overlaying of earth's substances over the fossil, and with the right combination, lead to fossils. It would still occur today, let's say you've buried a dog, and over time water, smelted rock, and a few other earth materials came over the dead dog's body. It would most likely be fossilized at the end of this process, but it would take years for it to happen. Fossilization does not happen in one day.