As far as I know, "under" is always a preposition. In your sentence, this can be confusing because the object (stress) is not a physical object, "under stress" is a little bit metaphorical.

Sorry, can't tell you what part of grammar 'under' is in this sentence - not my strong point. But I can tell you that the correct way to phrase your question is - Please tell me what kind of word "under" is here.

In the above sentence, which parts of speech does the word under apply, "prep, adv, adj?"

In this sentence, "under" is not a preposition. "under" is an adjective. Under means: subject to the control or effect of a person, drug, or force:(在…的控制之下) I know how much stress you've been under recently. 我知道你最近承受着太大的压力。 When "under" is used as an preoposition, it describes the position or location and means you are "underneath some person or thing." (under the table) When "under" is used as an adjective, it describes control or effect and means you are being control or effected by a person or thing. (The patient was under as soon as he breathed the anesthetic.)