Answer

1. The medieval authorities (Rishonim) already discussed this. Nachmanides on Taanit 15a brings two reasons: 1. We do not have ordained religious courts, and therefore there is no Torah-level stringency of a fast when there are no ordained judges. 2. There is no nasi (a governing authority; the community is not really a community). So too in the Ritva on Taanit 12b and Pesachim 54b, and likewise in the Raavyah, vol. 3, Laws of Fasting, sec. 854. See also Birkei Yosef, sec. 575:3. Still, there is some status to a decree issued by the sages of our time. See here for details.
2. Regarding sounding the blasts nowadays, see several explanations in the Mishnah Berurah, sec. 576:1.
As for an individual fast, in principle it does apply nowadays. See details here.
3. One can say that the reason for the commandment has lapsed, but even when the reason lapses there is still a problem with changing halakhot that were established by a religious court when we have no religious court today (except in cases involving harm, and a few other possibilities hinted at in the Tur regarding legumes). The same is true regarding requests and expressions of thanks in prayers generally. It seems to me that one can simply use those opportunities to connect with the Holy One, blessed be He (without counting on salvations).
Incidentally, Rabbi Abraham Isaac Kook writes in several places that changes which appear technical (there are no death penalties, there are no Amalekites, and the like) have an essential reason behind them (usually not conscious even to the sages who enact and interpret them). So perhaps today the fasts are not practiced for a technical reason, but behind that there is an essential reason why this is no longer relevant nowadays.
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Questioner:

1. According to this, why don't the sages of the generation issue decrees for fasts during wartime or during rocket fire on the country?
2. I have come to know some Lithuanian Haredi people whose children were sometimes sick with severe and serious illnesses (which would seemingly require a fast), and I don't recall that they took a fast upon themselves (maybe they didn't tell me). Does that mean they neglected a Torah-level positive commandment?
3. As far as I know, this Jewish law was not established by a religious court, but rather it is Torah law. And with Torah laws, the rule "if the reason lapses, the enactment does not lapse" does not apply. Fine, with regard to the Amidah, which was established by the sages, there is no possibility of canceling it. But with a Torah law, why shouldn't we cancel it where the reason has lapsed?

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Rabbi:

1. Because they know that this is not the right path for the public today. Once we are dealing with halakhic policy rather than strict Jewish law, it has to be evaluated according to its benefit. But in difficult situations they did try to institute or decree such things (there is also the question of authority: who would issue the decree and enact it?).
2. The question is what counts as a severe enough situation to require fasting. I do not know whether there is a halakhic definition for that. I have not checked whether the phrase "just as" in Maimonides is meant to extend the Torah law. Offhand, it seems to me that he does not mean to say that this is a Torah-level positive commandment.
3. With Torah law, we do not derive the reason for the verse in a way that would change the law, and that is parallel to canceling an enactment because its reason has lapsed. And again, there is also a problem of authority, since a matter established by formal count requires another formal count to permit it. However, for Torah law, the annulling body need not be greater than the one that established it, but it would still have to be a Sanhedrin.