Can Kato the Arm give himself his own buff? Since it does not say other friendly unit?

No, Kato the Arm cannot target himself with his triggered ability.

His card text states: "When I move to a battlefield, give another friendly unit my keywords and +[M] equal to my Might this turn."

According to the rules of language in Riftbound, the word "another" explicitly excludes the source of the ability (Kato the Arm himself) from being chosen as a valid target. Even if the text did not use the word "another," Rule 355.9.c clarifies that abilities and their sources are separate objects, but the specific wording on Kato's card creates an exclusionary targeting restriction that prevents him from buffing himself.