In other words, do they have the responsibility (or obligation) to see to it that the fourth Varna do what they had to do reap just rewards in this life and the afterlife?
Since learning and renunciation are denied to the 4th Varna - they are essentially denied spiritual advancement through their own effort.
Are there any penalties laid out for Dvijas who shirk their responsibility to uplift the fourth Varna?
Is it the responsibility of the dvija castes to teach the fourth varna rigteous conduct?
Yes, Shudras would serve a Brahmana master, and in turn, the Brahmana would teach him about Dharma, God, and how to perform Pakayajnas and Sraddha.
1.103 - This [the scriptures] may be studied with care, and duly taught to pupils, by the learned Brāhmaṇa,—not by any one else.
For mere wealth and material comforts, Shudras can serve Kshatriyas and Vaishyas:
10.121 - The Śūdra, seeking a livelihood, may serve the Kṣatriya; or the Śūdra may seek to subsist by serving a wealthy Vaiśya.
But for Dharma and spiritual merit, he should serve Brahmanas:
10.122 - He shall serve Brāhmaṇas either for the sake of heaven, or for the sake of both [wealth]; when, he has attained the title of the ‘Brāhmaṇa,’ this implies the accomplishment of all his purposes.
10.123 - The service of the Brāhmaṇa is described as the distinctive duty of the Śūdra; everything else that he does is fruitless for him.
10.124 - They [Brahmanas who are served by Shudras] should provide out of their family, a suitable maintenance for him, after considering his own capacity, and the man’s skill and the burden of persons to be supported by him.
Shudra receives welfare from Brahmanas who he serves:
10.125 - Remnants of food and worn-out clothes shall be given to him; as also the grain-refuse and old furniture.
Shudras are not obligated to rites, but they have the option to if they want good results after death:
10.126 - For the Śūdra there is no sin; nor is he worthy of any sacraments; he is not entitled to any sacred rites; but there is no prohibition against sacred rites.
He can perform certain yajnas called the Pākayajñas, and also śrāddha:
Gautama (10.64-65).—‘If permission has been given to him, the Śūdra may use the syllable namaḥ as his mantra. Some people declare that he may himself offer the Pākayajñas.’
Gautama (4.64). - ‘He shall perform the Pākayajña rites’
Yājñavalkya (1.121).—‘Devoted to his wife, pure, supporting his dependants, devoted to the performance of śrāddha, he should not omit to perform the fire sacrifices with the syllable namaḥ as his mantra.’
Shudras who want to acquire lots of Punya should imitate the practice of righteous men:
10.127 - If those who, knowing their duty, and wishing to acquire merit, imitate the practices of righteous men, with the exception of reciting the sacred texts, they incur no guilt; they obtain praise.
And from other scriptures:
Viṣṇupurāṇa (Parāśaramādhava-Ācāra, p. 419).—‘It is only through attending upon the twice-born that the Śūdra becomes entitled to perform the Pākayajñas; and thereby becoming blessed, he wins the worlds.—The Śūdra also shall make gifts, and perform the Pākayajña-sacrifices, as also the rites in honour of Pitṛs.’
Mahābhārata—Anuśāsana (Do.).—‘Finding the Śūdra oppressed with bad traits due to the quality of Tamas, Pitāmaha ordained attendance upon the twice-born as his duty. Through his devotion to the twice-born, the Śūdra drops off all those traits due to the quality of Tamas; and by attending upon the twice-born, the Śūdra attains the highest good.—Harmless, devoted to good deeds, worshipful towards gods and the twice-born, the Śūdra becomes endowed with all the rewards of Dharma.’
Mahābhārata—Śānti (Parāśaramādhava-Ācāra, p. 420).—‘The syllables svāhā and namaḥ are the mantras prescribed for the Śūdra; by means of these shall the Śūdra offer the Pākayajña-Sacrifices; he shall never amass wealth; having acquired wealth by service, he shall win the affection of his elders; and if he is righteously inclined, he may make gifts when permitted to do so by the King.’
Yājñavalkya (Do., p. 419).—‘Attached to his wife, pure, supporting his dependants, devoted to the performance of Śrāddhas, he should never omit to perform the Five Sacrifices by means of ths mantra namaḥ.’
There are no such responsibilities on the Dvijas.
Manu Smriti 4.80. Let him not give to a Sudra advice, nor the remnants (of his meal), nor food offered to the gods; nor let him explain the sacred law (to such a man), nor impose (upon him) a penance.
Also, it is not at all necessary that a low caste man will be entirely devoid of knowledge about good conducts etc just because he is low caste.
Because Manu Smriti clearly says that Dharma, good conducts, Subhasitas etc can be learnt even from a low caste person.
2.238. He who possesses faith may receive pure learning even from a man of lower caste, the highest law even from the lowest, and an excellent wife even from a base family.
2.239. Even from poison nectar may be taken, even from a child good advice, even from a foe (a lesson in) good conduct, and even from an impure (substance) gold.
2.240. Excellent wives, learning, (the knowledge of) the law, (the rules of) purity, good advice, and various arts may be acquired from anybody.
The first responsibility of the brahmins was to do tapasya with severe austerity and acquire Brahmajnana. 'Brahmanasya tu deho ayam na bhogaya kadachana' ( a brahmin's life is meant for penance alone).
Such brahmins no longer seem to exist. Moreover Swami Vivekananda quotes a Sloka from our dharmashasras that says that if a brahmin stays for some years under mlechchha rule, he becomes fallen. ( Lectures from Colombo to Almora by Swami Vivekananda). So who will teach whom?
Second, for becoming a real Brahmana, and take the respinsibility to teach or guide others, has to attain Brahmajnana. Otherwise it will be "Andhenaiva neeyamana yatandhah"(blinds being guided by a blind) as God says in His Gita.
Sri Chaitanyadeva mentions in Chaitanya-Charitamrita:
কিবা শূদ্র কিবা বিপ্র ন্যাসী কেনে নয়। যেই কৃষ্ণতত্ত্ববেত্তা সে-ই গুরু হয়॥
kiba sudra kiba vipra nyaasi kene nay/jei krishna-tattwavetta sei guru hay.
English Translation: Whoever has known God is able to be a Guru, be it Sudra, or Brahmin or a monk.
The Tantras also say that someone who has known God can initiate anybody. No rules are to be followed by a Siddha(Reference: Sastramulak Bharatiya Shaktisadhana, Upendrakumar Das, Vol.1).
Bhaktamaal also gives such references. According to the most common belief, Sant Ravidas, who was treated as being to very low caste, was the Guru of Meerabai.
