"I read the book."
This question is ambiguous in English, and not very natural. If the English says "I read the book" it could mean I read now, or I read earlier (past tense). But, "I read a book" is not normally how we would say "Ninasoma kitabu". Instead, we would say "I am reading a book". So, if the desired answer is "Ninasoma kitabu", I would suggest the English be corrected to "I am reading a book".
Saying "I read a book" (generally) with a present or tense agnostic meaning is unnatural in most contexts.
Yep. The simple present of verbs that describe actions (as opposed to states, such as "need", "love") generally represents a habitual action. Because book is singular, past tense is the most natural interpretation.
hapa pia wenzetu msahihishe hili jibu. unaposema "I read the book" kwa kiswahili sanifu itakuwa " nilisoma kitabu" bali unaposema "ninasoma kitabu" huna budi kuandika "I am reading the book" kwa lugha ya kimombo. au vipi wenzangu?