On average, how often one could encounter an adventurer in a world the details of which are written below?
Roughly 13 people per square kilometer overall, with up to 55 in the biggest cities. (about 15% increase compared to our medieval population)
There is noticeably fewer farmers for the reasons I'll explain later.
Most of the population lives in the smaller kingdoms, followed by "empires" (biggest are the size of Holy Roman Empire) and city states.
The goverments of most realms is in the hands of one ruler, a ruler with a council, or is an oligarchy.
The medieval hierarchy is still a thing, but not as strict, since individuals can go up that ladder quite a lot thanks to magic.
There still is quite a lot of land to be discovered/explored (some of these lands are what's called "forgotten realms", no connection to D&D books, which were abandoned due to a curse, long-lasting disease, or some other apocalyptic event that made the land unhabitable).
Technological level is somewhere around 1400s, but with some exceptions from further (sometimes much further) down the line.
Examples of what exists or not: Not-so-primitive guns do exist; magical street lamps light the richer city districts at night; banks are a thing; sewers are not a rare sight, even in medium-sized cities.
Theoretically it's everywhere to some extent, and many use it in day-to-day life, but since "with everyone super, no one is", the Magic is a thing of few. (one or two actual witches, sorcerers or priests is the usual for a village)
Magic can be measured by how many "normal" peoples' work someone could do, with 40% of the society being "normal" in terms of workforce, 30% being 22.5% more effective, every fifteenth - 52.5% and one in a hundred being able to work more than twice as effective, which puts the productivity of an average person at about 120 percent of a "normal" one. (hence less farmers needed)
Beasts, monsters and other threats
Beasts are highly magical individuals of an animal species, which developed abilities to live absurdly long compared to other of thier kind. On average an animal is considered a beast after it reaches a century (scales with the usual lifespan of a particular species). Beasts are significantly more dangerous than non-evolved specimen, but thier aggresion does not rise much, unklike with monsters. Also, all dragons are beasts.
Monsters are beings particularly violent and aggresive, but often not as dangerous as beasts. The most common type of monsters are animals possessed by parasitic and/or predatory spirits. Vampires, Demonic , Warped creatures, all fall into that category. And while technically skeletons and zombies are golems, they're too considered as monsters.
In the "Other" category there are things like golems, treants, demons and "civilized" threats (bandits and such). Other than undead, which are very prone to being animated by "dark" spirits, golems are a neutral threats, since they usually don't care for organic creatures. On the other hand, treants care very much for thier "herds", and wild ones can be very territorial. As for the last one, one must be the most wary about the most "civilized" individuals, because goblin bandits and raiders (not all are those, after all) are cowardly, and prefer their own skin over gain, unless under a tyrannical ruler.
Unpredictability and chaotic nature of magic has a chance of causing such event, which can render the land unusable sometimes even for centuries.
Large/powerful settlements have a rather nasty effect of attracting such events more the bigger they are.
Individuals and small groups are more respected, due to potential major power difference, and power distribution is very chaotic with magic.
Other than trade and surface connections, bigger communities can be quite reserved to outside, since one slip-up of power/information can have devastating consequences.