Is it common in English?
They are fairly common. By that, I mean if you use such terms, you won't get a lot of raised eyebrows.
Are there more examples?
Collins lists "break dancing" (with a space) as a noun. It also has it without the space. Collins also lists "Christmas shopping" as a noun.
Then there are these: bird-watching, whale watching, binge drinking, binge eating, skinny-dipping
Note that the terminology or how you identify the modifier will depend on how you use the compound words in a sentence.
For example, in
"They are Christmas shopping" and "I am bird watching right now"
both "Christmas" and "bird" are acting as adverbs modifying the verbs "shopping" and "watching" - these are present participles.
"Are you done with you Christmas shopping" and "I love bird watching"
both "Christmas shopping" and "bird watching" are nouns.
In "shopping is fun"and "I enjoy shopping", "shopping" is a gerund. See Is “shopping” a noun, verb or a gerund?
I think context is essential to understand what these sets of words are working as.
Note that I am not certain that this holds true for every example, as EddieKal mentions in their comment.