Here is a concise, traditional Jain understanding of the two topics you asked about.

1) Mahavira’s attain­ment of Nirvana (moksha)

• Where and when: According to Jain tradition, Bhagwan Mahavira attained Nirvana at Pawapuri (Pavapuri), in present-day Bihar, India.
• What happened: Nirvana means removal of all karmic bonds and the soul’s liberation from the cycle of birth and death. After attaining full awakening and having taught the Jain path for many years, Mahavira left his mortal body at Pawapuri.
• Important note on dates and traditions:

- The commonly cited tradition places this event around the 6th century BCE, with various Jain sects dating it to roughly 527 BCE, though exact dates differ among Digambara and Śvētāmbara accounts. - Digambaras and Śvētāmbaras agree on the core event (liberation of Mahavira) but differ in some chronology details and ritual interpretations.

• Core meaning (arth): Moksha is the complete shedding of karma and the final release of the soul from the cycle of rebirth. It is achieved by right faith, right knowledge, and right conduct, culminating in perfect liberating insight.

2) Gautama Swami’s kevala jñāna (omniscience)

• Who is Gautama Swami: He is traditionally regarded as the chief disciple (Ganadhara) of Mahavira and one of the principal early Jain mendicants.
• Kevala jñāna: Kevala jñāna means absolute, all-encompassing knowledge. In Jain doctrine, a liberated soul or a perfected kevali has this complete insight.
• When Gautama Swami attained kevala jñāna:

- There are two broad traditional positions: - Some traditions say Gautama Swami attained kevala jñāna during Mahavira’s lifetime, as the foremost disciple who had completed his own spiritual unfoldment. - Other traditions place Gautama’s kevala jñāna after Mahavira’s nirvāṇa, as a later realization within the nascent Jain sangha. - Because Jain texts and sects differ in chronology, these viewpoints are both present in classical Jain literature.

• Important note on tradition:

- Digambaras and Śvētāmbaras sometimes differ in the emphasis or sequencing of events surrounding the early disciples, including Gautama’s attainment. The essential point in all is that kevala jñāna represents perfect, omniscient knowledge attained by a liberated soul or a perfected human.

In short:

• Mahavira’s Nirvana: liberation of Mahavira at Pawapuri; moksha from the cycle of birth and death.
• Gautama Swami’s kevala jñāna: Gautam Swami is believed to have attained kevala jñāna as a principal early disciple; the exact timing (before or after Mahavira’s Nirvana) is treated differently in Digambara and Śvētāmbara traditions, but both agree on his attainment of ultimate knowledge.

If you’d like, I can present the core Sanskrit or Prakrit sutra wording related to these events and give the traditional glosses (arth) as found in Jain scriptures, keeping to the Digambara/Śvētāmbara distinctions.