Questions about sick sentences

The first sentence should be "blue and white painted on the plain embryo, and the brush strokes will fade", and after repair, it should be "blue and white painted on the plain embryo, and the brush strokes will fade" or "blue and white painted on the plain embryo, and the brush strokes will fade". Personally, it is not a sick sentence to omit poems and songs properly for the sake of rhythm without affecting the meaning.

The second sentence is "We all have a home-the name is China", and the second half sentence "the name is China" is a supplementary explanation of home. There should be no language error in this sentence (perhaps because of improper punctuation? ! )

I don't quite agree with your understanding of the second sentence upstairs. In the second sentence, I only admit punctuation mistakes, leaving out dashes indicating complementary relations. After adding a dash, it is a complete sentence without any language defects. It is also said in daily oral English that dashes should be added in general writing.