That breakdown looks correct.
A “clause” is basically a complete sentence within a sentence. To identify a clause, it helps to think of the sentence as a tree. To think of the sentence as a tree, it helps to break it down into units, or “constituents”. For instance, each of the 4 segments you look at is a constituent. Base on this, we can draw that part of the sentence in tree form:
| | |
| NP |
| _____|____ |
N S N V
| /\ | |
日本語の 時を表す 副詞を 学びました
Don’t worry about where to put the particles (there are highly technical reasons why they go with the nouns).
While the constituent analysys gives you the shape of the tree, it does not tell you what each node of the tree is. To do this, I start at the bottom and work up.
Hopefully, you can identify what part of speech each individual individual word is. The first problem is identifing what 「時を表す」 is. Notice that this end with a verb, and is followed by a noun at the next layer up. In Japanese, the only place a verb can go is at the end of a clause, so we know 「時を表す」 must be a clause.
Next, lets look at what 「時を表す副詞を」is. Since, 「副詞」is a noun, and the entire phrase just modifies 「副詞」, we can conclude that the entire phrase is a noun. Similarly, in 「日本語の時を表す副詞」We are just modifying the noun phrase 「時を表す副詞を」with 「日本語の」, so we again have a noun.
The next problem is what to call the entire phrase. In general, the reason this is a verb phrase is fairly technical, and probably not useful to know (as in, there are linguists who would disagree with this assessment). In this case, we can see it because in the entire sentence, it is being modified by the adverb 「昨日」. We can also guess this because Japanese is very “right-headed”, meaning that the classification of a constituent is based on the right-most element in it. For example, all of our noun-phrases had either a noun or a noun-phrase as their right child. Similarly, the entire phrase has a verb as its right child, and is a verb phrase. This doesn’t always work. For instance, a noun-phrase+verb-phrase could be either a verb-phrase or a sentence. In fact, you might notice that 「日本語の時を表す副詞を学びました」would be a complete sentence, except for the fact that it is preceded by 「私は昨日」.
I hope this makes sense. I tend to spend more time explain Japanese to my linguistics classmates than I do to my Japanese classmates, so might have gone a bit overboard on the technicalities.