If you haven't already, please see What should one do to help Israel during war?.
We are all dazed and struggling to find the words. We also don't want to just say nothing, so I guess I will make an attempt, for me, and if it happens to speak to anyone else...
Did you know that we are not allowed to ever listen to any music1? This is part of a series of halachot that we are commanded in to ensure that we are always mourning.
So, we are already always mourning, for the recent tragedies and those that are past. If our leaders ask us to take upon ourselves extra mourning like fasting and teshuva, then that is our avodah. As you have said, they have not done so (some Rabbonim have been organising selichot). This might be because they are looking back at the Yom Kippur War, and our leadership at the time told us to not fast, but rather to continue doing the avodah of Tishrei: be b'simcha.
Being b'simcha is a real avodah right now, because it is so hard2 - yet it is so vital. Your opening paragraph captures the feelings of all of the nation and that proves how hard it is. In the merit of this avodah, and the tzara it takes to perform this avodah, as well as the additional learning, mitzvot, prayer, tzeddaka and chesed, we can tangibly help the situation. Literally, a learning a pasuk can save a life! I would argue that being b'simcha can also save a life. If everyone you know is crying, what can make you have hope? But if there is even one person who is able to be positive, optimistic, unwavering and reassuring, they will light up everyone around them and that also can literally save lives.
This is anecdotal but I will say I've heard it dozens of times now from Jews everywhere around the world. The very moment they stood up and started helping each other was the moment they were able to cope and deal with the trauma. For some the chesed will be going and packing food, or helping someone with their baby, or shopping for batteries and blankets for the IDF. For others it is additional Torah and mitzvot, kavana and tefillot. We are all obligated to inspire each other, especially our bretheren in Eretz Yisrael, with courage and hope.
We are not victims3, we don't rot in yi'ush, and we feel the fear without letting it paralyse us, so let's keep the mourning in our hearts and carry on, until our leaders tell us otherwise. Let's just get up and do what our nation does best: serve. Time to serve each other, our brothers in danger, our family and friends, and our God. This will accomplish more than any amount of mourning can accomplish, and will show the world how bright a light unto the nations we really are, who never give up hope that the mourning will end forever.
1. See this article, which lists the leniences that some follow
2. Explained better than I can in this shiur by Rabbi Paltiel
3. Rabbi Manis Friedman commented in a recent (very refreshing, and unique) Q&A to someone who said they were finding it hard to daven and learn, that part of the problem could be that it feels absurd to our core that we should be sitting and begging for our lives. And this is right: it is absurd. We are a miraculous nation, who Hashem describes every individual as to Him like the only child to elderly parents. We are not learning and saying tehillim out of begging, but out of the conviction that we are mighty, and we are giving our might through learning and davening to tangibly helping our nation, and the world.