A possible answer to your first question is that it's a blessing to each person individually from God. It's not a group blessing.
Also the blessing is for each person listening. The blessing is talking to you personally.
I asked one of my teachers why the gender is not changed for a girl and he answered me that one should not change it. It's a passuk from the written Torah so it should be left exactly as it is, exactly as God said it.
There are numerous other answer to your first question, I'll try to collect some:
The Lenchener noted that the priestly blessing is said in the singular. The greatest blessing that the Jews need is one of unity.
Rabbi Dovid Goldwasser: One explanation is that it is not always possible, or wise, to give everyone the same blessing. For example, rain may be a blessing for a farmer but a hindrance for a traveler. Only G-d knows precisely what blessing is appropriate for each of us. He therefore tells the Koheinim to bless the people in the singular; each person should receive the form of blessing that is most appropriate for him/her.
Rabbi Moshe Leib teaches that the Kohen's blessing is in the singular, rather than the plural, to highlight that the greatest blessing is togetherness; when the Jewish people feel that we are one unit, in this itself there is great blessing. It is easy to focus on the differences between people and to view yourself as separate from others. Truly no two people are alike. But, there are many common factors among people. By focusing on the fact that every person is created in Hashem's image, we will have greater identification with others, which will lead to greater unity.
Although the Kohanim are indeed blessing the entire congregation, they do so in the singular in order to indicate that G-d desires to bless the Jews with the unity that results when love prevails. Thus, in the berachah, the Kohen is announcing his fulfillment of Hashem's command to bless K'lal Yisrael "be'ahavah" — "with love."