user151: 

Has the Buddha taught anything about how one should approach fixing society?




Does the Buddha advocate for striving to make society better?




Does the Buddha have any practices for groups and societies that would lead society to less suffering?




Does the Buddha have any teachings about Justice and  Social Justice?



user11009: Yes.
The best is the sutta on World Turning Monarch (DN 26).
In addition other two important sutta are Sigalovada Sutta (DN 31) and Parabhava Sutta (Snp 1.6).
There are many other suttas on the values of a great country.

user19480: 
Does the Buddha have any practices for groups and societies that would lead society to less suffering?

I do have an answer for this part, from Tibetan and Ch'an Buddhism, found in a Terma teaching passed on by the tertön Jamyang Khyentse Chökyi Lodrö. This teaching is about what happens-—and the suffering it causes-—during the Dharma-ending time (now).

Ananda pleaded with the Victorious One:


“Victorious One, because you consider things with great compassion, spare humankind this torment.”


And the Victorious One replied to the venerable Ananda:   "I have this to say about it. While I was residing in the great expanse of space, I was thinking of and gazing on the beings of the world. So, listen! There is a teaching useful during the time when the dark age arises. If one writes of it, propagates it, and practices the "Great Responsiveness Meditation" and recitation, impurities and obscurations will be quickly purified. If one sincerely makes offerings to this spiritual text with flowers and incense, all sentient beings will benefit. By propagating this text and writing about it, one will obtain a good existence throughout all of one's lives."

The full English translation, from which the above quote is taken, was done by Stephen B. Aldridge  (Ka-rma gSung-rab rgya-mtsho) with the assistance of Ngor Thar-brtse mKhan-po, bSod-nams rgya-mtsho Rin-po-che. It is available in full in my article “Jamyang Khyentse Chökyi Lodrö's Prophecy of Things to Come”
Great Responsiveness Meditation is the practice used by Avalokitasvara (referred to as “the One Who Hears the Cries of the World” in the following quote) to become enlightened, which Manjurshi asserts is the best practice for all of us today:

Great Assembly! Ānanda! Halt the puppet show Of your distorted hearing! Merely turn your hearing round To listen to your genuine true nature, Which is the destination of the Path that is supreme. This is the genuine way to break through to enlightenment.  


It is the way that the innumerable Buddhas followed Straight to nirvana's gate. All Thus-Come Ones of eons past Succeeded by this method. Through this method, Bodhisattvas, Too, right now are gaining perfect understanding.


Among the people of the future, those who undertake A spiritual practice should rely upon this teaching. I myself became enlightened by this very method. He Who Hears the Cries is not the only one.
  
The Buddha, the World-Honored One, made a request That I consider methods that will rescue beings Who in the Dharma's ending-time resolve their minds Upon attainment of transcendence and nirvana. The best of all the methods is the practice Taught by the One Who Hears the Cries of the World.


The sages who attained enlightenment by other means Were aided by the Buddha's awe-inspiring spiritual power, And each was specially taught how to abandon all affliction. Some of these paths are shallow, some go deep; these teachings vary.  


I bow now in respect to all the Buddhas, and I bow To all their Dharma-treasuries and to the marvelous ones Who've put an end to outflows. And may beings of the future Be empowered so that they will have no doubts That this one method is the most accessible.  


It is the easiest way to reach enlightenment. It is the teaching most appropriate For Ānanda and for the beings drowning In the Dharma's ending-time. They only need This practice of the faculty of hearing For them to break through to enlightenment, For it surpasses all the other methods. It is the genuine path to the true mind.⁠(taken from: “The Śūraṅgama Sūtra,” Buddhist Text Translation Society, 2009, pgs 253-257)


user14277: Research "engaged Buddhism." It is a movement within Buddhism that was started by Thich Nhat Hahn and addresses this specific question.

151: <blockquote>
<blockquote>
<p>Has the Buddha taught anything about how one should approach fixing society?</p>
</blockquote>
</blockquote>
<blockquote>
<blockquote>
<p>Does the Buddha advocate for striving to make society better?</p>
</blockquote>
</blockquote>
<blockquote>
<blockquote>
<p>Does the Buddha have any practices for groups and societies that would lead society to less suffering?</p>
</blockquote>
</blockquote>
<blockquote>
<blockquote>
<p>Does the Buddha have any teachings about Justice and  Social Justice?</p>
</blockquote>
</blockquote>
 11009: <p>Yes.
The best is the sutta on World Turning Monarch (DN 26).
In addition other two important sutta are Sigalovada Sutta (DN 31) and Parabhava Sutta (Snp 1.6).
There are many other suttas on the values of a great country.</p>
 19480: <blockquote>
<p>Does the Buddha have any practices for groups and societies that would lead society to less suffering?</p>
</blockquote>
<p>I do have an answer for this part, from Tibetan and Ch'an Buddhism, found in a Terma teaching passed on by the tertön <em>Jamyang Khyentse Chökyi Lodrö</em>. This teaching is about what happens-—and the suffering it causes-—during the Dharma-ending time (now).</p>
<blockquote>
<p>Ananda pleaded with the Victorious One:</p>
</blockquote>
<blockquote>
<p>“Victorious One, because you consider things with great compassion, spare humankind this torment.”</p>
</blockquote>
<blockquote>
<p>And the Victorious One replied to the venerable Ananda:   &quot;I have this to say about it. While I was residing in the great expanse of space, I was thinking of and gazing on the beings of the world. So, listen! There is a teaching useful during the time when the dark age arises. If one writes of it, propagates it, and practices the &quot;<strong>Great Responsiveness Meditation</strong>&quot; and recitation, impurities and obscurations will be quickly purified. If one sincerely makes offerings to this spiritual text with flowers and incense, all sentient beings will benefit. By propagating this text and writing about it, one will obtain a good existence throughout all of one's lives.&quot;</p>
</blockquote>
<p>The full English translation, from which the above quote is taken, was done by Stephen B. Aldridge  (Ka-rma gSung-rab rgya-mtsho) with the assistance of Ngor Thar-brtse mKhan-po, bSod-nams rgya-mtsho Rin-po-che. It is available in full in my article “<a href="http://bit.ly/TheLightThatMakesThingsClear" rel="nofollow noreferrer">Jamyang Khyentse Chökyi Lodrö's Prophecy of Things to Come</a>”</p>
<p>Great Responsiveness Meditation is the practice used by Avalokitasvara (referred to as “the One Who Hears the Cries of the World” in the following quote) to become enlightened, which Manjurshi asserts is the best practice for all of us today:</p>
<blockquote>
<p>Great Assembly! Ānanda! Halt the puppet show Of your distorted hearing! Merely turn your hearing round To listen to your genuine true nature, Which is the destination of the Path that is supreme. This is the genuine way to break through to enlightenment.  </p>
</blockquote>
<blockquote>
<p>It is the way that the innumerable Buddhas followed Straight to nirvana's gate. All Thus-Come Ones of eons past Succeeded by this method. Through this method, Bodhisattvas, Too, right now are gaining perfect understanding.</p>
</blockquote>
<blockquote>
<p>Among the people of the future, those who undertake A spiritual practice should rely upon this teaching. I myself became enlightened by this very method. He Who Hears the Cries is not the only one.
  
The Buddha, the World-Honored One, made a request That I consider methods that will rescue beings Who in the Dharma's ending-time resolve their minds Upon attainment of transcendence and nirvana. The best of all the methods is the practice Taught by the One Who Hears the Cries of the World.</p>
</blockquote>
<blockquote>
<p>The sages who attained enlightenment by other means Were aided by the Buddha's awe-inspiring spiritual power, And each was specially taught how to abandon all affliction. Some of these paths are shallow, some go deep; these teachings vary.  </p>
</blockquote>
<blockquote>
<p>I bow now in respect to all the Buddhas, and I bow To all their Dharma-treasuries and to the marvelous ones Who've put an end to outflows. And may beings of the future Be empowered so that they will have no doubts That this one method is the most accessible.  </p>
</blockquote>
<blockquote>
<p>It is the easiest way to reach enlightenment. It is the teaching most appropriate For Ānanda and for the beings drowning In the Dharma's ending-time. They only need This practice of the faculty of hearing For them to break through to enlightenment, For it surpasses all the other methods. It is the genuine path to the true mind.⁠(taken from: “The Śūraṅgama Sūtra,” Buddhist Text Translation Society, 2009, pgs 253-257)</p>
</blockquote>
 14277: <p>Research &quot;engaged Buddhism.&quot; It is a movement within Buddhism that was started by Thich Nhat Hahn and addresses this specific question.</p>
