In asking why Esther asks for her life first, the Maharal actually strengthens the question by pointing out that her life was not being threatened at this point at all since the king did not know she was a Jewess. Even if he were to know and include her in the decree, she still would not need to mention herself independently, since she would then be logically included in the general category of Jews.
Rashi answers that Esther felt she should have been killed as per the decree.
R’ Dovid Feinstein explains that she knew Achashverosh had more sympathy for her.
The Dena Pishra adds that Eshter was saying that she cares about Achashverosh’s good above all else. Convincing this evil tyrant through the paradigm that concerns him – his own selfish wants – she is explaining that killing the Jewish people would cause him to lose his greatest supporter, herself. Similarly, he continues, Esther implied that, as she was innocent, so too are all of the Jews innocent.
Yosef Lekach and R’ Moshe David Valle point out that Esther asked for her life as a minor request, and the people as her major plea. From her perspective, her own life was not as important as the life of her nation.
R’ Yehonason Eibshutz quotes the Talmud (Shabbos 148a) that a she’aila is for the short-term present, whereas a bakasha is for the long-term forever.
The Ginzei HaMelech quotes the Midrash (Shemos Rabba 30:4) that since Esther risked her life for the Jews, the Jewish people are called “Esther’s people.” Although this Midrash is commenting on the verse (Esther 4:16) about her risking her life by appearing before Achashverosh uninvited, Esther risked her life in other instances, as well – as in this verse in which Esther asks for her life in a she’aila, as though it were something inconsequential and ephemeral in comparison to the existence of her people.
Earlier in Esther (5:6), the Malbim wrote that a request is just a request, but a petition is the reason for the request. Therefore, her ultimate desire is for the people’s survival.
The Malbim also writes that Esther mentioned herself first to imply that she was Haman’s intended target.