I think this video is fictional but it got me to wondering if the Samurai and the early European explorers ever came to blows or fought as the other people's they met did.
To my surprise (and I'm sure to yours as well), the video was not fictional (well, mostly not). I'm assuming you've already googled and are just skeptical of the Wikipedia entries, so I'll just go through them and clear any potential myths or confusions. Truth be told, I've never even heard of either of these events. So research took me a little while. Both events seem to be in the realm of terrible documentation, and I could only find limited information.
1: The battle of Fukuda(ura). This is by far the hardest one. There is next to no records of the battle of Fukudaura in the Japanese language (aside from a few mentions there and then). There seems to be quite some more in English, but they were only just slightly more extensive. The video seemed to paint Dom Joao in a brave, never-wavering light (maybe that's just my feeling), but some scholars such as Hesselink interpreted his actions as idiotic and typical of the noblemen who only gained their positions through connections.
Now, did the event actually happen? Well, the historical background might be able to help answer that. The foreign traders (and Jesuits) did stay in Hirado after their exile (dramatically-speaking) from Satsuma. During this time, Matsura vassal Kodeda Yasutsune was converted, and the commoners within his region also converted. Defacement and destruction of local shrines took place under the new faith. Later, a religious debate held between the Kirishitans (Japanese Catholics) and local Buddhists led to a conspiracy to commit violence by the Buddhists. Matsura Takanobu ruled in favour of the Buddhists, and exiled the Jesuits as a punishment. The traders were allowed to remain, but this unfair judgement led to a lot of distrust between the Portuguese and Takanobu. Later a dispute between the local merchants and the Portuguese ones (Miyanomae incident) led to the departure of the latter in 1561.
Following their leave, the Portuguese were invited by Omura Sumitada (who later became the first Catholic daimyo) to continue trade in his territory, which escalated to a series of problems. Sumitada's conversion turned his vassals discontent, and this opportunity was used by the neighbouring Goto Takaaki to invade the Omura domain. Some sources (新編大村市史) stated that Takaaki's invasion was his revenge for Sumitada's defacement of his adoptive father (and Takaaki's real father, Omura Sumisaki) grave. It sure sounds like a good story, but the historical accuracy is questionable. Either way, Takaaki was ready to take back his father's land. The battle of Fukudaura took place in 1565, and Takaaki had just colluded with discontent Omura vassals 2 years prior, destroying the previous merchant port for the Portuguese, the Yokoseura. It seemed that the Omura was in a rather weak position, and an attack by the Matsura to rid Sumitada of his golden goose (like Takaaki did) would no doubt further the Matsura advantage. All these factors foster the conditions for the battle of Fukudaura. Overall, I don't see much reason to be suspicious of this battle's existence.
2: The 1582 Cagayan battles. This one was also a pain in the bum. While the existence of the incident is quite strongly supported by the historical documents (letters sent by Juan Baptista Roman) - a good majority of sources are either in Spanish or Portuguese, and the small amount remaining covered the event in its bare minimum (and sometimes held slightly contradicting points). Some accounts stated that the Wako pirates harassed the natives of Cagayan, and the Spanish attacked the Wako in an act of defence (whether for the benevolent protection of the natives or to secure the stability of the region and the trade). However, some others suggest that Cagayan was a settlement/territory of the pirates under the leadership of Tay Fusa (not "Tay Zufu", as the video mistakenly called) - and the Spanish attack might have been an act of colonisation into Cagayan - in-lined with their expedition into Cagayan for religious conversion just one year prior (in 1581). These two aren't necessarily mutually exclusive tho: the Spanish attack could be both for colonisation and retaliation to the harassment of piracy in nearby regions.
The video smartly did not mention the heavily disputed "epic last stand at Cagayan" (where 40 Spaniards supposedly defeated 1000 "samurai"), which had not been favoured by this article on Gunsen history and the video by Metatron.
Collectively, Gunsen history and Metatron pointed to the fact that the ethnic make-up of Wako had been highly debated. And, this is true: some proposed that a large amount of Wako were Koreans disguising as Wako (Tanaka Takeo/田中健夫) or commoners from Jeju island (Takahashi Kimiaki/高橋公明); some suggested that Wako were made up of a big ethnic multiplicity, including Chinese, Korean, and Japanese (Murai Shosuke/村井章介); and some pointed to the differences between earlier-stage Wako and later-stage Wako and their varying ethnic make-up (哲秀城). Overall, they were not samurai, and most likely had a relatively small proportion of Japanese people.
So - to conclude - both events likely did take place. However, while the battle of Fukudaura did indeed involve samurai, the battles of Cagayan most likely involved a very small amount of Japanese people, and of them none were samurai.
Sources:
THE PHILIPPINE COLONIAL ELITE AND THE EVANGELIZATION OF JAPAN (by Maria Fernanda G. de los Arcos), url: https://www.redalyc.org/pdf/361/36100404.pdf
「新編大村市史」 第二巻 中世編 三章, url: https://www.city.omura.nagasaki.jp/bunka/kyoiku/shishi/omurashishi/dai2kan/documents/2-3syou.pdf
16世紀 「倭蓮」を構成する人間集団に関する考察 -「倭」と「日本人」の問題を中心に- (by 哲秀城), url: https://opac.ll.chiba-u.jp/da/curator/900022816/Sh-H0068.pdf
The Dream of Christian Nagasaki: World Trade and the Clash of Cultures, 1560-1640 (by Reinier H. Hesselink), p. 37-39
edit: spellings, made it easier to read