Combat archeologist here (specialising in Slavic and Viking weaponry and warfare).

The Medieval Period spans over a millenium, and applies to a large chunk of the planet (EUrope, a part of Asia and northern Africa) so describing ALL warfare in it is beyond a mere Reddit post.

TLDR Description:

The basic "set" of medieval weaponry for a single combatant would be an axe, a spear, maybe a shield, sometimes javelins, or in case of bowmen; a bow and arrows plus an axe or a long knife/cleaver/kord.

Swords were much rarer (though not as rare as some historians would claim). The reason for that was that a sword was an expensive tool (financially, an eqivalent of a car today), required training to use properly, and, unlike a spear or an axe, had no other use in everyday life.

Remember, that most medieval combatants were not "professional soldiers" but (especially prior to the First Crusade) common men who were enlisted or volounteered to fight, with whatever they had to arm themselves. Actual warriors and later knights, were a minority.

In battles where good portion of the combatants actually WERE professionals (ex. Battle of Grunwald, Visby, Hastings etc) the % of swords was higher. Generally, the use of swords varied. Just at the dawn of the Medieval, swords were relatively common, and often cheaply made (to the point that pre-christian European pagan rituals often included bending swords and burying them with the dead, or throwing them into a sacred lake/swamp ). Viking/Charlemagne Era had seen a great improvement in the quality of bladed weapons, which translated in increased price. It remained stable throughout the centuries untill, circa 1400, the mass production of weaponry became realistic, and swords became cheaper again.

As for the size and shape, it varied greatly. Migration Period had swords of over 100cm, the Vikings and Charlemagne's time Europeans wielded ones measuring from 75 to 90cm. Over time, improvements in both weaponsmithing and armour -smithing allowed for stronger plate armor, and called for greater swords to crush it. Post the invention of the heavy crossbow (arbaleste) and the firearm, as well as pike tactics and cart-forts; plate armor became less useful, and so did big swords. This lead to the popularity of the rapier (which started as a typical sword and thinned over time) and a sabre (which is useful primarily in slicing unarmored oponents from horseback).

Axes varied even more than swords, partially because they doubled as a tool, and partially because their low status allowed for more leeway in the way they were smithed. It would be near impossible to describe or even name all types of axes used in the Medieval Era (even if we focused on just the Viking Era it would be still more than 18 types with infinite variations). One interesting form would be the Dane axe, a broad curve-edged one mounted on a long staff.

As for other "sidearm" weapons there were maces, clubs (often spiked), flails (which included the ball on a chain type, usually onehanded, and the two-handed type: two heavy rods chained together, like a giant noonchaku), as well as various hammers, mallets, cleavers, seaxes (long knives/single edged swords prefered by the Saxons and the Vikings) and many various devices that as well as the above, started out as common tools and evolved into a war-form. The same evolution happened to the polearms, which is given in their names like: war-scythes, combat-pitchforks, long flail (which started as a haybeater) , the glaive and the halberd (both started as tools used by lightermen and lumberjacks) etc.

As for the one-handed vs two handed weapons, both were popular, and necessary in a combat formation. For example, in a viking (as well as saxon, slav etc) shield formation, the shieldmen would be armed with one-handed weapons for obvious reasons. Behind them, the second line would be armed with long axes, spears, and other polearms, and both lines would protect the archers.

Post the introduction of plate armor, two-handed swords gained popularity, and in one form or another, survived untill the 17th century.

As for Medieval duels, those were usually highly standardised with rules governing who can use what kind of weapon and in what circumstances. Generally speaking, a duel between equals would call for at least technically equal armament (quality aside). Aside from the lances used in jousting duels, duelists used "regular" weaponry, and if anything, the armor would be different. However, only a tiny fraction of people would be able to afford a second armor just for duels.

Is the popcultural image true that the vikings and slavic nations had higher usage of axes?

Not exactly much higher, axes were very popular everywhere. However, by the time Vikings descended from Scandinavia, and the Slavs coalesced into a recongnizable group, Western/Southern Europe already had a proto-feudal warrrior class wirth specialised weaponry. The northern and eastern edges of Europe were more likely to recruit from among common men, which would be armed with axes. The differenc ehowever is not very prominent.

If you are interested in the topic of medieval war, warriors and weaponry , I greatly recomend researching the works of Oakshott, Petersen, and a quick peek through Osprey books (NOT the most reliable source, but enough to give you clues.)