During the Kamakura period, when the game took place, far more than just warrior elites were armed to some degree: multiple accounts of “commoners”—usually the citizens of an estate—hunting down bandits themselves survive (1). Likewise, the carrying of long swords by commoners was outlawed within the premises of the city of Kamakura, the shogunate seat, by law from 1250 onward. Being armed and able to engage in self-defense was therefore not the sole prerogative of the professional warrior, not to mention some aristocratic warrior elite.

But what is a professional warrior, or bushi, in this case?

For one, a specialist in riding and archery—and especially both at the same time: mounted archery (2). But furthermore, these bushi were members of the lower aristocracy invested with some kind of local office (e.g., jitō, geshi, azukaridokoro, kumon, etc.) which granted him rights to managing one or more localities, be these estates, villages, districts. And, of course, was attached to income in form of taxes and local labor by the residents.

Only the poorest of these warriors would have engaged in his business all by himself. They usually had several dependents: servants, serfs, and also subordinate warriors. There are multiple terms for the latter kind: rōtō and rōjū, amongst others. For all we know, these "non-noble" warriors were also specialists in the martial arts, just like their lords. They apparently also were typically mounted troops as well. However, since they did not possess an office like their lords, they were economically dependent.

For example, one document from 1276 lists the provisions supplied by one estate manager from Higo province for military use: himself (35 years old), one rōjū, three shojū (unfree dependents, unclear for which purpose), one horse, armor (one yoroi, one haramaki), two sets of bow and arrows, and a long sword (tachi) (3). Another document from the same year from Echigo province mentions the warrior himself plus two mounted (his brother-in-law and one young rōtō, which here is categorized as a wakatō) and seven foot soldiers, although with less detail (4). (I should note that documents mentioning these things are exceedingly rare for this period, and the latter document appears to be the only document explicitly mentioning foot soldiers by their names)

In summary, there were definitely more than just upper-class bushi, or samurai, involved in military affairs before the Sengoku period, especially during the time of the Mongol Invasions.

The number “80” stems from historical accounts of the time; however, this number doesn’t refer to eighty “samurai,” but more accurately, to ca. eighty mounted warriors including rōjū; apparently all Sō Sukekuni, the shugo of Tsushima could muster in the spur of the moment: he had to traverse a distance of twenty miles to the beach once he had received word of foreign ships approaching. He also apparently wasn’t entirely certain what was to come: it is said that he first dispatched a messenger (conversational in Chinese) towards the fleet to ask of their purpose, but the poor soul’s boat was greeted with arrows instantly, and multiple boats proceeded to land, attacking the riders on the beach (5).

I think that—if we believe the records—your second question should be self-evident (its not a question of “would they?”, but “do I believe the sources are true?”). We can assume that when the Mongols landed, these men only had the choice of either:

- doing their duty and thus upholding their family honor (despite it meaning certain death), which, incidentally, was the "right" choice in consideration of the economic security of their kin.

- running away (since, apparently, there were a few survivors, those likely retreated)

- simply surrendering (not sure I'd consider this a viable option after the messenger I sent to parlay got slaughtered).

As for the third, I’m not exactly sure what the intent of your question is.

During the early medieval period, war wasn’t exactly all that common. If we look at the Kamakura period, after the Genpei War and its follow-up, the destruction of the Ōshū-Fujiwara (which, together, rendered the 1180s a decade of war), the only “major” conflicts were the—very short—Jōkyū War in 1221 and the Mongol Invasions in the late 13th century. Certainly, the Kamakura period also saw a few uprisings, mostly by remnants of the Heike, and several localized conflicts involving not more than a couple hundred people. For this reason, the typical warrior official wouldn’t exactly see much action beyond hunting down robbers, bandits, and pirates—in other words: doing police duty.

Only when society became more unstable after the Kamakura shogunate fell, conflicts also increasingly saw a reliance on larger forces comprised increasingly of foot soldiers in ever larger quantities, which arguably reached its high-point during the Sengoku period.

Now, explaining why a professional warrior class even existed that occupied a significant share of local and provincial offices (which invested them with the authority to prosecute, judge, and police the countryside) and not some commoner militia, is an entirely different matter.

Nevertheless, I hope it's become apparent that there were more than just warrior aristocrats involved even before the Sengoku period.

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(1) For example, the Konjaku monogatarishū contains such an anecdote. See also Kamakura ibun, doc. 20603, for another incident where a robber is shot to death by villagers.

(2) There are numerous books touching on this subject out there; the copy I have at hand would be Kimura Shigeaki, Chūsei shakai no naridachi, Tokyo: Yoshikawa Kōbunkan, 2009.

(3) Kamakura ibun, doc. 12275.

(4) Kamakura ibun, doc. 12276.

(5) Unfortunately, my in-depth books on the Mongol Invasions are at my office; hence, I referenced Seno Seiichirō, Mōko shūrai, in Komonjo no kataru nihonshi, vol. 3: Kamakura, edited by Yasuda Motohisa, Tokyo: Yoshikawa Kōbunkan, 1990, pg. 197–246, here: 208–210, for an account of the Tsushima-landing. I would like to note that this figure might omit non-mounted troops which might also have been been present, since this reference only speaks of mounted troops; however, I would require the primary source itself to examine the exact phrasing used here. If I recall correctly, William Wayne Farris (somewhere in Heavenly Warriors) once suggested that, for this period, on every cavalryman, two or three foot soldiers should be assumed to be present.