Learn English – “Because of” and “Due to” after adjective

It depends on intonation. With a certain, emphatic intonation, Tom looks pretty tired can mean "Tom looks very tired; indeed, his level of tiredness is remarkable." With ordinary intonation, it just means "Tom is moderately tired—tired enough to matter, but his level of tiredness is not especially remarkable."

The emphatic intonation that I have in mind drags out each syllable of pretty to an equally long length, about as long as the word tired. The pitches go something like E D C, like "Three blind mice". Of course, there are many other kinds of intonations and emphasis that a person could give the words, suggesting many different kinds of tiredness, and there is no precise, standardized code. You just improvise.

Most of the time, the names aren't particularly inventive.

"Шапка-невидимка" — a hat which, being put on, makes a man invisible;

This would probably be an invisibility hat or hat of invisibility, compare to a cloak of invisibility (which is quite a common item).

"Сапоги-скороходы" — self-running boots;

Compare with seven-league boots, which make each step cover 7 leagues of distance (38.8km). Also compare with the winged sandals of Hermes in Greek mythology.

"Скатерть-самобранка" — a table-cloth which produces all sorts of meal and drinks according to its user's preference;

I don't know of anything common that's similar to this, but it did remind me of the Land of Goodies from Enid Blyton's The Faraway Tree books – the Land of Goodies is a place where everything is made of delicious food.

"Ковер-самолет" — a self-flying carpet;

Just a "flying carpet" or "magic carpet" in English. I imagine most people would think of Aladdin when you mention flying carpets.

"Живая и Мертвая вода" — the two kinds of water, one called "alive" and the other — "dead". The former heals the hero's wounds, the latter revitalizes him;

I haven't heard of anything like this. Something more general would be potions, magic concoctions which may have any number of effects. The term "elixir" is also for liquids which heal and give strength.

"Молодильное яблоко" — an apple which, having been eaten, turns the old into the young.

Not a food, but compare with the Fountain of Youth, which is a fountain which makes young anyone drinking or bathing in its waters.

As for common English folklore, a very common story is Jack and the Beanstalk, where a young boy (Jack) barters for magic beans. During the night following the beans being planted, a giant beanstalk grows. At the top of the beanstalk, Jack finds a large castle inhabited by a giant. Jack steals from the giant, and the giant chases him down the beanstalk. Jack then fells the beanstalk, killing the giant and living happily ever after on his ill-gotten riches.

The phrase "happily ever after" is also a common element in many English-language folk stories.

An element in Scottish folklore is the kelpie, a water spirit that lives in lochs that is said to have the strength of many horses. These are particularly noteworthy due to the massive statue called The Kelpies that was built in Falkirk.