Just to address the specific sources mentioned in the OP:
I. Shulchan Aruch EH 37:8 (Hebrew link):
It is a commandment for a person not to marry off his daughter when she is a minor, until she grows up and says, "I want [to marry] So-and-So."
The unusual phrasing that the Shulchan Aruch (Rabbi Yosef Karo, 16th century) uses ("it is a commandment") may suggest a less than absolute prohibition to marry off one's minor daughter. To shed light on Rabbi Karo's specific meaning in this case, see his commentary on Maimonides' (12th century) legal codes (Kesef Mishne, Hil. Ishus 10:16, Hebrew link):
[Maimonides:] If someone gives his minor daughter to be betrothed, and her groom demands to finalize the marriage, she and her father are each able to prevent the marriage until she grows up and becomes a na'ara maiden.1 If he2 wants her to be married, he can marry her off, but it is not appropriate to do this.
[Rabbi Karo:] It appears that our rabbi [i.e., Maimonides] inferred from that which it says in the Talmud (Kiddushin 41) that "it is forbidden for a person to marry off his daughter when she is a minor," that "forbidden" was meant non-literally. Rather, the Talmud means that it is inappropriate to do so. This interpretation is consistent with the baraisa (K'subos 57b): "She and her father can each prevent the wedding." This implies that if both she and her father are willing, it is [technically] permitted. Maimonides3 also wrote this in Chapter 3: "Even though a father is permitted to marry off his daughter when she is a minor or a na'ara maiden, it is inappropriate to do so. Rather, it is a commandment of the Sages that a man not marry off his minor daughter," etc.
II. Rabbi Ya'akov Emden, 18th century (Sh'eilas Ya'beitz I, §14, Hebrew link):
For us, whether regarding the kiddushin [the first stage of marriage] and certainly regarding the nisu'in [the second stage of marriage], it is unacceptable to conduct this with an actual minor.
This is the concluding line in the responsum, quoted in the other answer.
III. Aruch HaShulchan, 19th century (EH 37:33, Hebrew link):
Our rabbi, author of the Shulchan Aruch, wrote in EH 37:8: "It is a commandment for a person not to marry off his daughter when she is a minor, until she grows up and says, 'I want [to marry] So-and-So.'" [The Rama, Rabbi Moshe Isserles, adds in his gloss:] "And there are those who say that nowadays [i.e. in the 16th century and the prior few centuries] it is practiced to marry off our minor daughters because we are in the Exile, and we don't always have the means to fully provide the dowry. Also, [the Jewish people] are few in number and we can't always [readily] find a suitable marriage partner. And it is customary [to accept this lenient opinion]."
But in our days, we do not marry off minor daughters, and we have never heard of someone marrying off a minor daughter. And this is correct, for in the Talmud (Kiddushin 41a) it is brought that it is forbidden to marry her when she is a minor. And while it could be that it is permitted if she is amenable (Chelkas M'chokeik EH 37:10), this is nevertheless not correct. And this is the practice that has spread in our time in our countries [i.e., not to marry off minor daughters].
1 See fn. 3 in the original answer
2 I.e., the father; an alternative version reads this as "they", i.e., both the father and the daughter, which better conforms to the context of the passage - see Chelkas M'chokeik EH 56:6 (Hebrew link)
3 Ishus 3:19, Hebrew link.
