Xyooj said:
it's sci-fi, does it has to be correct?
it's about imagination more than reality?
That question is more about story construction and story intention than about physics.
If you are writing abstract, "soft" SF or even fantasy, then it doesn't matter whether you put your civilisation
inside the sun, as long as it contributes fundamentally to the story. If it is not essential to the story then do not sully the writing with irrelevant nonsense;
leave it right out! It does not contribute to the story and destroys the suspension of disbelief. For horrible examples read almost any of the teenage crud on the Internet, and a fair proportion of popular published SF of the mid-to-late 20th century. For good examples read Vonnegut, much of Wells, Wyndham, Tolkien, Stevenson, or classical mythology for example. Or Browning's Pied Piper of Hamelin.
OTOH, if you are writing hard SF, like some of the works of Wyndham, Wells, Niven, Clement, Clarke etc. then you must omit every item that can possibly be omitted whether scientifically arguable or not, but those details that are of interest to the story must be either accurate and defensible, or clearly speculative (is there really liquid water on... Can we really find a drug or treatment that... etc) because otherwise it not only fails to contribute to the story, but destroys the suspension of disbelief as well.
What you certainly cannot do as a competent writer, is to say: "Oh, it is only a story, so it doesn't matter what sort of #$%^&* I write; it is up to the reader to enjoy it." That would hardly work for Jane Austen at one extreme or Evelyn Everett-Green at another, let alone SF.
In general, SF is fiction in which the science matters; if it doesn't matter it shouldn't be in the story; matter extraneous to ANY story should be omitted, leaving non-technical fiction. If it does matter it should be as real and convincing as possible.