My experience with turning then necking down is that I can adjust my turning cutter to just barely cut, and it will only cut the high side. Meaning that although I turned the necks to the exact same thickness all the way around before necking down, the necks were no longer uniform thickness after necking down. That’s not to say that it will matter to you. If it does matter to you, you will probably need to turn the necks after necking down. If you’re turning a lot, you might turn them first, neck down, and turn them again.
I always recommend annealing after necking down. I built a wildcat and was shooting it with a fitted neck, so not working the brass at all, and started having split necks after only 2-3 reloads. I annealed all my brass and have over 10 loadings on some of it since that point and have neither annealed a second time, nor lost a case to a split neck. From then on I annealed my brass any time I necked up or down, and haven’t had any trouble. I don’t know how common it is when necking up or down to split necks so quickly, but I do a lot of brass prep, and don’t want to loose cases, so I just anneal and don’t worry about it.