1) 酸菜 suān cài
2) 榨菜 zhà cài
3) this view of the package doesn't say what it is.
4) Don't know, but it appears to be Taiwanese. It says 高采 gāo cǎi (literally 'tall vegetable'.)
Of your original 6, the Chinese characters are
1) 橄榄采 gǎn lǎn cǎi - I've never known this to contain mustard, though. It is Chinese olive paste.
2) and 3) as above
4) 芽菜 yá cài
ya cai
5) 雪菜 xuě cài
xue cai
6) 天津冬菜 tiān jīn dōng cài
As you surmise, there are several other mustard preparations.