If God is the healer, why go to a doctor?
The blessing ends by calling God the healer of the sick. So is medicine optional? The Gemara answers from a verse. Shemot 21:19 says a person who injures someone must pay for his healing. The Hebrew doubles the verb: verapo yerape. The school of Rabbi Yishmael (early sages, from the time of the Mishnah) read that as: the Torah gave a doctor permission to heal (Bava Kamma 85a).
The Gemara also records an argument about how to pray before treatment. Rav Acha taught a prayer for someone about to be bled, a common treatment then. It says: You are a faithful healer, and Your healing is true, since people do not really heal, they are just used to it. Abaye objected: do not say it that way, because the Torah gave doctors permission. Rashi (the main Torah commentator, France, around 1100) explains Rav Acha's view like this: they should not have taken up medicine, only asked for mercy (Berakhot 60a).
The Ramban (Nachmanides, a Torah commentator who lived in Spain and died in the Land of Israel around 1270) describes an ideal. When the people are fully faithful, God keeps sickness away, and they do not need a doctor. But people became used to medicine. Once someone is sick and comes for treatment, the doctor should not refuse. Ibn Ezra (a Spanish commentator of the 1100s) reads the verse more narrowly. The Halleluyah prayer for Tehillim 146 tells his view.
The Shulchan Aruch (the main code of Jewish law, from the 1500s) rules without that hesitation. Healing is permitted, it is a mitzvah (a commandment), and it counts as saving a life. A doctor who holds back "sheds blood," even if someone else could treat the patient (Yoreh Deah 336:1).
So the sources do not set prayer against medicine. They differ on how to describe the doctor's role. Rav Acha, the Ramban and Ibn Ezra each describe it differently, and the Shulchan Aruch records the ruling.
Shemot 21:19,Bava Kamma 85a,Berakhot 60a,Ramban on Vayikra 26:11,Ibn Ezra on Shemot 21:19,Shulchan Aruch, Yoreh Deah 336:1Why does it say "us" when I am asking for me?
The first line is a verse, and in the verse it is singular: "Heal me, Hashem, and I will be healed" (Yirmeyahu 17:14). The siddur turned "me" into "us." Abudarham (a commentary on the prayers, written in Spain around 1340) notices the change and asks whether it is allowed.
He cites an earlier rabbi's answer: there is a rule against changing a verse from singular to plural when you are reading it as Scripture. But a verse you use as a prayer is a prayer, and may be adjusted to the moment. Rabbeinu Yonah (a Spanish rabbi of the 1200s) adds a limit: if you say a whole psalm in order, do not change it. The Rosh (a leading rabbi in Germany and Spain, who died in 1327) agrees.
That settles the technical question. It does not say why "us" is better. The Gemara has a teaching that points the same way: "Anyone who asks for mercy for his friend, and needs the same thing himself, is answered first" (Bava Kamma 92a). It gives two proofs. God restored Iyov (Job) when he prayed for his friends. And Avraham prayed for the household of Avimelech, a king he had dealings with, to be healed, and right after that the Torah says God remembered Sarah (Bereishit 20:17 and 21:1). The Gemara says this about prayer in general. It does not mention this blessing.
The siddur still gives you room to name one person. The Rema (Rabbi Moshe Isserles of Krakow, whose notes on the Shulchan Aruch record Ashkenazi custom) writes, quoting Rabbeinu Yonah, that for a real personal need, like a sick person at home, you ask in the singular, not the plural (Orach Chaim 119:1). The printed paragraph does something related. It names one sick person, and then places that person "among the other sick of Israel."
So the siddur has two layers. The blessing asks for everyone. The paragraph inside it names one person.
Yirmeyahu 17:14,Abudarham, Weekday Prayers, Amidah,Bava Kamma 92a,Rema, Orach Chaim 119:1If I pray for someone and they do not recover, was it wasted?
Nothing in these sources promises a cure. They show both answers, even for the same person praying.
Moshe cried out five words for Miriam. God's reply: she must stay outside the camp for seven days, and then she may come back (Bamidbar 12:13-15). Another time Moshe begged to enter the Land of Israel. God told him: "Enough. Do not speak to Me again about this" (Devarim 3:23-26).
King Chizkiyahu (Hezekiah) was told by the prophet Yeshayahu: "Set your house in order, for you will die and not live." He turned his face to the wall and prayed. God sent Yeshayahu back: "I have heard your prayer, I have seen your tears. I am adding fifteen years to your life" (Yeshayahu 38:1-5). In the Gemara he says he has a family tradition: even if a sharp sword is resting on a person's neck, he should not hold back from praying for mercy (Berakhot 10a).
Rabbi Chanina ben Dosa, a sage known for his prayers for the sick, would pray for patients and then say: "This one will live and this one will die." Asked how he knew, he said: "If my prayer flows smoothly in my mouth, I know it is accepted. If not, I know it is rejected" (Mishnah Berakhot 5:5). In the Gemara he adds that he is no prophet, only passing on a tradition (Berakhot 34b). Notice that his own sentence expects some patients to die.
These sources do not explain why one prayer is answered and another is not. What they give is an instruction: do not hold back from praying, even when it looks hopeless. The Asher Yatzar prayer looks at a related question, why people get sick at all.
Bamidbar 12:13-15,Devarim 3:23-26,Yeshayahu 38:1-5,Berakhot 10a,Mishnah Berakhot 5:5,Berakhot 34b