You set range, speed, bearing, and course of the enemy, then adjust the numbers over time as you never get them right the first try. Ships have mechanical computers (about as big as a fridge) that have knobs you turn on them for those settings, and they give you a running solution to lead the enemy, and that is how the turrets are aimed.
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4. Speed. Again, takes time. You guess at first
Not in this game - ships always move at the same set speed, as you note. And that's the problem with completely realistic fire control for ship guns - like our hyper-accurate laser-guided bombsights, it makes it way too easy because the things that made it difficult in real life aren't modeled in the game. Our ships don't even roll! And then there's wind, air temp and pressure at different altitudes, which had to be guessed, age and other variables that affected powder performance, barrel wear... long-range ship gunnery is like shooting a rifle at 1000 yards: all sorts of things affect it that are small enough to be ignored at 100 yards, so it becomes a completely different skill.
I think the old sea mode was about right in difficulty - an experienced gunner could get hit rates well above historical ones even in controlled conditions, but the nature of this game kinda demands more decisive action in less time than IRL.
They also have radar, which makes using the periscope system just a backup.
I won't swear to this, but believe the radar was generally the backup for surface gunnery when visibility was good - the optical systems were more accurate, and at least in early and mid-war the crews were better trained at using the optics. Radar range finding was a huge advantage to the allies at night and in bad visibility, when they used it properly - but often they didn't, as at Savo Island. IIRC the Axis powers developed search radar but never developed radar fire control or rangefinding (I'd imagine anything concerning naval surface warfare was very low priority for the Germans after 1941).
