The water in mires is also safe to drink, and in the latest version there are now springs, too, which are also safe.
It's good that you looked up the salinity in the Baltic sea. In general, "would this work in real life" is a good guideline for if something will work in the game. You can die of thirst in a few days but it does take some weeks to starve to death. Definitely finish the tutorial course, it'll give you a good intro to stuff you'll need to know. Try all the things you can think of to try and get a feel for which things you find the most fun. Hopefully you'll enjoy at least one way of feeding yourself.
Before hunting, drop most of your stuff at your campsite -- or even just on the wilderness map, and use F6 to make a marker of where that is. You'll get less fatigued running if you're not carrying too much.
If you have a house, you can smoke meat in summer. If you don't have a house, you can borrow the fireplace of a village. You can also use salt to preserve a lot of meat but that is more expensive. In winter, you can hang meat to dry next to a shelter.
Big game don't spawn on very small islands, but you may get some in winter if the ice forms a bridge to a larger island.
Many plants don't provide enough nutrition to keep you from starving, but some of them are better when cooked. Uncooked, only cloudberries and lake reeds are worth it. Ember-roasted turnips are also better than nothing. Barley and rye are very nutritious once cooked into bread or porridge. Other plants may have medicinal properties or they may be useful as baits for fishing. You always want to use a bait while fishing with a rod, even if it's just some leaves. With the leaves, you will be able to catch some small fish, and the small fish can be used as baits for catching big fish.
It is very cold in winter, and you can die of hypothermia very quickly if you fall into water or if you are away from a fire for too long without adequate clothing. If you fall through the ice, wield a sharp weapon in each hand, it'll make it easier to climb back onto the ice, and then stay on your belly and crawl off the ice. The ice can support you better while lying down.