If we are talking ship-to-ship combat then generally no, modern battleships took a lot of punishment before actually sinking. An example would be Bismarck which had pretty much it's entire superstructure shot away and took multiple torpedo hits before actually sinking.

However, less modern battleships would prove terribly vulnerable in WW2. A lot of the ships involved were WWI vintage due to the naval treaties in effect prior to the war. This meant that you had some rather old (although modernized) ships participating in battles against modern weapons.

The british battleship(well battle-cruiser) HMS Hood was sunk in the opening minutes by the Bismarck/Printz Eugen in the battle of the Denmark Strait. It's speculated that a shell from the Bismarck somehow hit a magazine on the Hood blowing up the ship with nearly all hands. Hood was built towards the end of WWI.

Another example could be the Japanese battleship Fuso (from 1912), she was struck by aerial bombs and torpedoed in the battle of the Surigao Strait and sunk. So this might perhaps count as sinking after taking a few hits.

In conclusion, yes, they could sink to one very unlucky shot, or they could do as designed and survive tremendous punishment.

As others have given you an ok idea of the amount of damage a capital ship could take (depends a LOT on everything from type of damage, damage control practices, conditions of the ship).

For time though it varied even more wildly. You have Denmark Straight, essentially the smallest major ship action of the war and it was concluded in less than 30 minutes from sighting to the end of firing with both sides essentially breaking it off when Prince of Wales turned away.

But you had then North Cape of similar size which lasted over 10 hours due to weather and attempts by Scharnhorst to flee.

The same variation also came up in carrier actions. It was all about a convergence of weather/time of day, when the enemy was found and location confirmed, how damaged the fleet and air wings were damaged, and the objectives of the commanders.

For instance while the fleets maneuvered for about 3 days in the area, the Coral Sea's main action took place in one afternoon/evening and the following morning and early afternoon.

Midway then just a month later was resolved in the space of about 8 hours then and much more decisive.