Ever since I first came up on it, the ranges at which battleships battled it out amazed me. One question I have though - how visible was the enemy fleet during most of the battle? Would an average sailor on the deck be able to see that they've just hit an enemy, or would he need some binoculars to do it? I mean this purely in context of engagements between fairly large ships, like the battle of Jutland.
Also, another question: could sailors determine that their ship is about to be hit/attempted to be hit by looking at the muzzle flashes on enemy ships? If yes, were there any reports of this causing panic or loss of morale on board?
Battleships and battlecruisers of the time had their central aiming equipment as far up in the ships tower as possible, a considerable height above the waterline, so the visible range at which ships engaged isn't just from the height of a person above the surface. As long as these elevated fire control stations could see part of the target and the splashes from their shells, gunnery was technically possible. Anyone using the fire control optics would be able to see the enemy vessel, as well as hits and incoming fire, in good weather and lighting. However, effective range was a bit less, as at extreme ranges small differences in the alignment of the guns, weather conditions, and even the rotation of the earth made shooting inaccurate. Even at effective range, the average sailor on the deck would most likely not be able to clearly see the full outline of the enemy as well as hits (and also, nobody would even be on the deck in the first place when the big guns were shooting.) Not all combat was at maximum effective range, and closer targets would absolutely have been easily visible (such as the Blucher at the Battle of Dogger Bank.)
In the coal-burning era of WW1, funnel smoke was a big consideration for visibility and gunnery accuracy. If the wind was blowing towards the target, or if it was dusk and the sun was setting on the opposite side, visibility could be reduced. The worst nightmare of a gunnery control officer was to be blindly shooting at the flashes of the enemy guns through the murk, as happened to the British at the Battle of Coronel.
For your last question, remember that at long ranges, accuracy was fairly poor, and the shells could take upwards of 20 seconds to reach the target. There was a lot of missing involved as the fire control tried to get the range right, so at long range it's not as if sailors could see the enemy guns flash and know that their doom was incoming. However, many people described the feeling of watching the shells coming in (often visible because of their size) as very eerie and unnerving, even if they were odds on to miss. I would definitely recommend "Castles of Steel" by Robert Massie about this topic- it's a fantastic and readable overview of naval combat during the war, and includes some of those descriptions I just mentioned. I don't have it with me at the moment and can't quote them, unfortunately.