UUU (btw. good to use simply given and more comfortable to use such names, it gives the questioner and answerer more seriousity, who would sacrify normaly to a UUU and have not certain discomfort with it?) and who ever also seriously interested, here in short but selfexpanding if going deeper, answers to the single questions:
Did the Buddha teach some measure of "Engaged Buddhism", to maybe more of a lay person audience?
In regard of being a perfect disciple, he praised people who teach and also act according the Dhamma most. But one is also fine in just carrying about himself, since the Buddha knew that circumstances and possibilities of being are different and had no illusion of creating a "good" and peaceful Samsara.
Sikkha Sutta: Trainings
This sutta is one of a series explaining AN 4.95, which rates individuals of four types. The lowest is the one who doesn't practice for his own benefit or for the benefit of others. Higher than this is the person who doesn't practice for his own benefit, but does practice for the benefit of others. Higher still is the person who practices for his own benefit, but not for the benefit of others. Highest of all is the person who practices both for his own benefit and for the benefit of others. Thus, as explained in this sutta, it is best if you not only follow the precepts but can also get others to follow them as well.
In regard to a layman's relations he gave advice to be secure in all directions: Sigala- sutta, The Layperson's Code of Discipline
In regard of community duties and engagements, he set out rules only for the Sangha of Monks and mostly very voluntary to take on. Most is a matter of duties in relation between teacher and disciples: Cv 8: Vatta Khandaka — Collection of Duties but even in teaching Dhamma by monks the prefix "I a monk wishes..." is always present, so it was of most interest for him, that people strive for their own liberation also for monks. Yet not to speak of his non-encouragement in getting additional burdened for laypeople how have already enought duties out of their dependency and dealing in society by themselves.
Did the Buddha ever teach "Engaged Buddhism" to the Bhikkhus?
No at all, not in the way it is generally understood. A Bhikkhu is not asked to help in any way with outwardly things but more over, out of good reason, limited and "discouraged" to help in usually wordily ways, since it would make the path for liberation invisible for many in that way.
Making a living provide a favor for supporter in giving wordily help and assistance like sadly many popular monks do, the Buddha called "animal art" and such is a heavy offence and corruption. How ever, in some cases Bhikkhus are allowed to give also help in frame of food, cloth, shelter and medicine if having or ask for such, but that is restricted to people like father and mother or people near the Sangha and training. (See also under politic and taking side below.)
Even in regard of being engaged in helping by teaching the Dhamma, there are cases where the Buddha called those who have not gained something lasting for themselves, called Bikkhus "worthless monk" to provoke to do the real desk fist: The Story of Thera Potthila
He encouraged sometimes disciples of him, who have reached at minimum Streamwinning, e.g. Noble Ones, to teach the Dhamma for release of engagement, liberation, if willing and able. A encouragement given to his disciples who have all already gained path and fruits or even liberation, which is often "misused" by so called "Dammaduta"-monks, monks who teach or even missionaries engaged in improper ways putting often Vinaya on the second place for doing so.
He also mentioned that it is good to approach and rebuke sectarians from time to time, like the householder Anathapindika once did and of course always praised the gift of Dhamma.
Not and nowhere it will ever accrue as a duty to "rescue" others, at least because it's not possible. Those with less dust in the eyes how ever, have all possibilities to follow and receive support.
What Buddhist scriptures support Engaged Buddhist teachings?
Some, or better most, take certain rebirth stories as indirect encouragement, but the Buddha did not teach to follow his non-perfect history but provided the best way for one self and all others with the engagement in the Noble Eightfold path.
All scripts supporting such are later and defiled developments of those not seeing benefit of ending engagement in a wheel of causing suffering for one self and all others.
Is it proper for a Bhikkhu to be political in anyway in the world or in the monastery?
Not at all. It's either corruption, meaning that one maintains his livelihood and supporters with such and taking side, a heavy offence: Saṅghādisesa 13, or it is simlpy strong wrong view of a Bhikkhu, not understanding the aim and purpose of the holly life. Everybody is goid advised a avoid political involved monks and those monks taking on side, which ever side it might be. Such a person, a person with wrong view, is no admirable friend or teacher for a good and also not a place for having much benefit of ones gifts.
Did the Buddha teach Engaged Buddhism?
Yes, he likes you to be full engaged in the best you can do for you self and all other being, in accessing and walking the Noble Eightful Path with your actions in mind, speech and bodily deeds and he does not like you to just talk about it and think how it would be but to put it into action as your whole life's purpose if ever possible and willing to do something beneficial for your self and all others.
Having abounded engagement but fully being engaged in his path, you become a real hero and not another fool not seeing the arrow placed in the own heart.
If having additional question, feel being given to ask also here, since it allows more independence of engagement in the world and its aims.
Since this a good lesson for those with eyes and the strong impermanence of comments, Atma likes to add a short discussion from another good and proper answer in words.
Maybe worthy to add the "duties" of engagement of them: The ascetics and brahmans thus ministered to as the Zenith by a householder show their compassion towards him in six ways: (i) they restrain him from evil, (ii) they persuade him to do good, (iii) they love him with a kind heart, (iv) they make him hear what he has not heard, (v) they clarify what he has already heard, (vi) they point out the path to a heavenly state. http://zugangzureinsicht.org/html/tipitaka/dn/dn.31.0.nara_en.html if liking to add
– Samana Johann 2 hours ago
You have read this teaching incorrectly. The teachings states: "thus ministered to as the Zenith by a householder ". In other words, the householder first shows faith in the monk. I have no faith in you, for example, therefore it is sinful & a transgression of you to try to teach me. Regards
– Dhammadhatu 2 hours ago
Not sinful & transgressing Dhammaduta and good that you understood the teaching rightly, but called dukkhata and so not encouraged by the Buddha for his disciples to engage and of course it bears the danger of making disrespect in regard of the three juwels usual. So it seems two worlds, that of right and wrong view do not easy come together if not making sacrify at first place in faith. And as told, it's for the sake of those able to be healed that those who are lost also receive Dhamma. May it be an emergency hint.
– Samana Johann 14 mins ago
It's all a good sample for many think about "engaged Buddhism" here, so Atma hopes you can provide enough generosity to do not delete the more subtil teachings for low wordily sake as Dhammadhatu usually does, calling it "emptiness. Mudita in advanced.
– Samana Johann 9 mins ago
"Monks, even a monk who has long penetrated the Dhamma in this Doctrine and Discipline would do well to refute the wanderers of other persuasions with the Dhamma periodically in just the way Anathapindika the householder has done." Ditthi Sutta: Views Some sad "good that the teacher(s) are gone, now we can do as we like", some others simply knew that they had receiced a lot of goodness and walked without correcting the lost on in the foodsteps of gratitude.
– Samana Johann 4 mins ago
At the end, as a person who actually gave up all wealth, pleasure and gain to sacrifice all gifts to engage for the welfare of the "poor", meaning not only talk around, likes to share a usual proof of the Buddha before he gave leave to monks desiring getting dhammically engaged, usually not expected to live further for a long: Punna Sutta: An Punna (Puñña, one having merits)
So when you are really already in the position of Punna, and really able to bear all this and able to live exclusively on the goodness of others without calling for rights and demanding this or that: Go on and sacrifice that what you have righteously made to your own and share the accumulations you have gained being really your on and gifts. Be a great field of merits in this world so empty of possibilities for many.
You may find a maybe extended version as well as given space for discussion and further question, dedicated for the Sangha and their follower her. Fell given with strings only pulling torward Nibbana:
[Q&A] Did the Buddha teach Engaged Buddhism?
(Note: This is a gift of Dhamma and not meant for commercial purposes or other wordily gains.
There might be parts that have been edited by others. The fact of not reconstructing it does not mean to approve such by the author if not mentioned in a visible way. Sadhu for editing spellings and layout, Nyom Chris.)