Answer:
First of which makes more sense?
He living with friends in an apartment in HCMC since last week.
He has lived with friends in an apartment in HCMC since last week.
He lived with friends in an apartment in HCMC since last week.
He live with friends in an apartment in HCMC since last week.
Due to A & D not making sense in this statement, we can narrow the answers down to B & C.
Due to the sentence stating "since" we can tell that the person in this sentence is still living there so, just lived makes the sentence past tense whereas has lived is present tense.
So the answer is B