Regarding a woman going underwater in the sea:
You wrote that this would be a bedieved tevila even before nightfall.
Is this so even though there may be chatzitzes on her body and she is covered with a swimming costume?
I mentioned that there are a number of sefeikos involved, and this is one of the main ones.
Although it is certainly forbidden to perform a tevilah with a bathing costume, as written in Minchas Yitzchak (Vol. 4, no. 35; even bedieved, one may not rely on such a tevilah, because the costume is tight), Rav Moshe Feinstein (Iggros Moshe Yoreh De’ah, Vol. 4, no. 17, sec. 19, and Even Ha-Ezer Vol. 4, no. 14) writes that it is possible that tevilah with a bathing costume is effective, because the water penetrates the costume.