I think you may be falling trap to presentism and reading quite a bit of our modern-day assumptions about how time passes back into an earlier era. Keep in mind that there's a LOT to do aboard a ship at sea, especially aboard a merchant ship with few hands. Exploring ships and naval ships would have a lot more men (and women) on board, but the nature of military discipline means that there are a lot of make-work tasks done aboard ship to keep crews occupied.

Some of the daily tasks that sailors during the period that I studied embarked on would include:

• Rising before dawn for a quick breakfast; packing up your hammock and putting it in netting above deck

• Holystoning decks (think of scrubbing the decks with sand and water, on your knees, pushing a stone the size of a large Bible for the scrubbing action), washing them down, and swabbing them dry;

• pumping ship (wooden ships leak, a lot);

• repairing sails and/or rigging;

• making and mending slops (clothing)

• caring for livestock kept aboard;

• repairing the hull or ship's fittings;

• painting ship;

• setting up or striking topmasts;

• working as a blacksmith or armourer;

• hoisting in or out boats;

• cooking (each ship's mess had his own cook, who would add his own flair to what the ship's cook produced)

Officers would also have their own set of tasks, including standing watch, taking navigational sightings and calculations, keeping journals up to date, dealing with routine discipline and management issues, working in their particular areas of the ship, and lots of other tasks. And that's not even getting into actually sailing the ship -- trimming sails, laying aloft to set sails, getting new sails up from belowdecks or striking sails, and all the attendant time that took, without any mechanical aid besides capstans, block and tackle, and winches.

You can also add into that gun drill, small arms drill, drill with cutlasses and pikes, and all the attendant time it took to service guns and small arms.

And if you still have time left over after that, sailors would spend time making crafts, singing and dancing, drinking and socializing. Gambling was officially forbidden in the English/British navy, but it occurred regardless. Storytelling and music were important tasks for keeping up morale.

To get to some of your more specific questions,

Food. I guess it was just days after days of salted meat plus alcohol? Have they ever thought that their voyage might last longer than, say 50 days? How would they survive then? Fishing? What about drinking water?

Fishing, no. They would pack enough stores for their length of voyage. (The open ocean is basically a desert, compared to the marine life near shores.)

In the British navy, sailors were entitled to a daily ration of bread, some sort of meat (or a substitute on non-meat days), some sort of vegetable (often dried peas), and some sort of non-water drink, as well as water. There are a lot of myths about water and spirits aboard ship. From an earlier question I answered:

Now, that said, in the British navy it was the practice to embark beer or other alcoholic beverages as part of the sailors' daily ration. The "rum ration" as a defined amount per day can't be dated until 1844, but sailors certainly had access to spirits throughout the working day. During the period of the Napoleonic wars, which I am most familiar with, sailors would be issued a gallon of beer per day, but the beer ration became an enormous brewing/stowage problem over time. A third-rate ship, the smallest ship reckoned able to stand in the line of battle, would have to stow 50-100 tuns (~240-250 gallon units) of beer, which would come in large barrels called "butts" (half a tun) which themselves weighed half a ton (the weight measure) each. The volume and weight of those displaced other stores, so rum gradually replaced beer, especially for foreign service.

The spirits ration was half a pint (instead of a gallon of beer) and it became regularly issued in the morning and evening, mixed as "three-water" grog (three parts of water to one of spirits). Two pints of liquid would not be nearly enough for a working day, so we infer that sailors drank water in the intervening time. (There was also absolutely an illicit trade in spirits, but that's a separate issue.) The spirits ration could be stopped for small crimes, but spirits (or beer) were seen as an entitlement and stopping spirits or watering them were causes for discontent among sailors.

Moving to fresh water, then: water stored in wooden casks would certainly become slimy and unpalatable over time. Ships dealt with this by frequently re-watering (at streams or other fresh water sources), collecting rainwater, and by boiling water, but many sailors had to just tough it out (for lack of a better term). Iron water storage tanks mitigated those problems, but they were not in wide use until the end of the period I'm familiar with.

Much of a ship's fresh water would in any case be used for soaking salt meat (beef and pork) and cooking, not drinking. But free access to a barrel of water ("scuttle butt") is mentioned in a fair number of contemporary sources.