I encounter difficulties when drawing a syntax tree for a sentence of expletive contruction. Should I mark the dummy subject "there" as a noun? Thx
Good question! It depends on the details of your sentence.
For sentences like "it is raining" or "there is a rhinoceros", the dummy subjects "it" and "there" act for all (syntactic) intents and purposes like noun phrases. Basically, English syntax doesn't allow a finite verb without a subject, so it adds one at the syntactic level that doesn't exist at the semantic level.
For sentences like "eat the tuba", there's no subject visible on the surface, but it's clear that one actually exists on the underlying level: for example, look at "mail the pineapple to yourself". Reflexive forms like "yourself" only show up when there's something else referring to the same thing, in a specific place in the syntax tree. So there must be a "you" in the underlying model.
For sentences like "damn you" or "bless you" (or harder expletives if you prefer), it seems like there's no syntactic subject at all—even an implicit one. For details, see the legendary paper English Sentences Without Overt Grammatical Subject by "Quang Phuc Dong" (James D. McCawley), which points out that these expletives don't act at all like normal verbs and proposes an different analysis. (Basically, these are "quasi-verbs" which don't even form standard sentences at all: they only appear in the single production "Epithet → Quasi-verb NP".)