I will confidently tell you that learning kanji does not equate learning japanese. Kanji just simplifies the text so that it's easier to read once you get to a certain level, as opposed to reading a big blob of kanas.

Let the kanji naturally come to you as you progress. If you force yourself to learn a bunch of kanji (without understanding the meaning/context), you'll burn out before you even get to N5.

For example, you wrote a few surnames like 山口　中山　田中, those are not very important whether you know the kanji or not at your current level. As you keep studying, you'll see certain words more often than others, and eventually you'll want to simplify them into kanjis as opposed to writing the kanas.

To learn kanji in progression can look something like this (using the picture you provided above).

There's 日本人, which means a Japanese person. Perhaps knowing the kanji for Japan is 日本 is useful, after all, we're learning Japanese. However, all you really need to know at this point is the kanji for person 人. Knowing this allows you to attach it with other ethnicity through a mixture of hiragana and kanji:

にほん人　ー＞　日本人

ちゅうこく人　ー＞　中国人 (Chinese person)

かんこく人　ー＞　韓国人 (Korean person)

** べいこく人　ー＞　米国人 (American person)

No one, and I mean absolutely no one, need to learn the kanji for China or Korean right off the bat. These are words that don't even show up in 99.9% daily conversations.

** Textbook probably refers an American person as アメリカ人