I imagine Buddhism is about following the path and then, if you can, influencing others to follow the path. I imagine Buddhists such as the Buddha or Thailand's Bhikkhu Buddhadasa had the ability to influence political activists & leaders. When I lived in Bhikkhu Buddhadasa's monastery, I met the Thai Prime Minister more than once.
However, I think Buddhists can only lead by example and be careful about how they engage in political talk. For example, Thailand's Bhikkhu Buddhadasa influenced many Communists, where I imagine some of them were "martyred" in the 1976 Thammasat University Massacre.
For example, the Dalai Lama mingles within the corridors of world power but Dalai Lama appears to not actually influence evil politicians to change their ways. It is the opposite. The evil leaders appear to use the Dalai Lama to make themselves look better. Dalai Lama was paid US$180,000 per year for many years by the CIA.
Famous monks such as Ajahn Brahm often name-drop how they know this politician & that politician but, at least in Australia, the political environment moves further & further away from Dhamma each day. In fact, Ajahn Brahm maintains harmful & dangerous political narratives, such as the myth of 'Islamic terrorism' (which, in reality, is a UK-US-Saudi covert operation since WW1).
It was very unfortunate to witness the Western monks & nuns affiliated with Ajahn Brahm become politically active in Anti-Trumpism, where, even though Trump's anti-war rhetoric was obviously a lie (based on the Iran-Hater who was funding his presidential campaign); these monks & nuns were politically active supporting the major war maker Hillary Clinton & Obama, who destroyed at least three countries, namely, Libya, Syria & Yemen; plus escalated conflict in Ukraine & elsewhere.
Bhikkhu Bodhi openly lamented when Trump threatened to ban abortion. Bhikkhu Bodhi, appearing to pander to a liberal left-wing supporter base, somehow believes Buddhism supports "women's reproductive rights". While monks & nuns can plead ignorance & having no psychic powers when their political endeavors actually support covert wars, Bhikkhu Bodhi's political stance based on "women's reproductive rights" dropped the jaws of many Buddhists.
At least in Australia, recently, the religions, particularly the Catholic Church, were mostly silent about the international intervention in Syria, where covert terrorist squads murdered thousands of Christian & non-Christian people. The Christian religions in Australia were mostly silent when old Christian monastery towns were liberated by Syrian & Hezbollah defenders. This shows how narcissistic religion has become.
Today, there are Western monks grovelling to left-wing political correctness, such as attempting to appeal to the LBGT & Identitarian movements. Will siding with political correctness help Buddhism survive into the future? Or will this alliance harm Buddhism by wrecking its doctrine more than it is already wrecked in the West?
Ordinary people (puthujjana) look for affirmation in religion. They want a Protestant-style Jesus and an amoral metta Buddha to not judge or criticise them at all. Ordinary people (puthujjana) want to be justified by religious figures. Therefore, politics can easily wreck religions, such as Protestantism wrecked Christianity or Wahhabism wrecked Islam. When religion becomes mere amoral narcissistic metta, it becomes worthless. As Jesus said: "You are the salt of the earth but if the salt loses its saltiness it becomes worthless".
Often there is little we can do as Buddhists, apart from following the path and hopefully setting an example and possibly influencing others, high & low, if we can. But using the brute (military & police) force of politics - no - that does not appear to be Buddhist.
Therefore, to offer my opinion on the questions:
Yes, Buddhists can assist in creating the structures of a group or society, as long as that group or society accords with Buddhist doctrine.
Yes, Buddhists can embrace the established structures of a group or society, as long as that group or society accords with Buddhist doctrine.
Yes, Buddhists can assist defend others by enforcing the established authority of a group or society, as long as that defense & enforcement accords with Buddhist doctrine.
Yes, Buddhists can, without violence, push away or overthrow the established structures of a group or society, as long as that group or society accords with Buddhist doctrine.
Yes, Buddhists can defend others by pushing away or overthrowing the established authority of a group or society, as long as that new group or new society accords with Buddhist doctrine.
In other words:
Supporting Communism appeared not Buddhist.
Edorsement of violent Western imperialism appeared not Buddhist.
Supporting the myths of the $7 trillion taxpayer funded War On Terror against nations unrelated to the 9/11 attacks that kills & uproots millions of innocent people is not Buddhist.
Supporting psychopathic mass-murders who create deadly covert wars is not Buddhist.
Promoting abortion is not Buddhist.
Actively recruiting unsuitable people to Buddhism who may actually not be partial to the true teachings & thus attempt to change the true teachings, doesn't sound like it is Buddhist.