[me_jumper]

"China" is a term used for fine dishes made from porcelain as far as I'm aware (non-native speaker myself)

[ragtagtag]

In this case, I suspect "china" comes from Cockney rhyming slang, "china plate", "mate", as in "friend".

[re]

No, it's referring to the tableware -- every word in that position for all the phrases is a container of some sort (or at least a thing that can contain other things).