• ādyam-puruṣam — the original Supreme Person
  Phrase: ādya (first, original) + puruṣa (person). Sūta uses one of the Bhāgavata's high titles for Kṛṣṇa at the moment the brāhmaṇa first sees Him — the verse classes the meeting as a darśana of the Ādi-puruṣa, not merely an audience with Dvārakā's king.
• pratīhāraiḥ-praveśitaḥ — brought inside by the gatekeepers
  Compound + participle. The dvāra-pālas of Dvārakā are themselves residents of Vaikuṇṭha-rank; their function as gatekeepers is structurally the same as Jaya-Vijaya. The brāhmaṇa is conducted in by qualified servants — Vaiṣṇava etiquette mirrored into the architecture.
• kāñcana-āsane — on a golden throne
  Compound: kāñcana (gold) + āsana (seat). The verse's aiśvarya-register is foregrounded — Kṛṣṇa receives the brāhmaṇa from a throne of gold. Gauḍīyas read this as the doctrinally correct context for Rukmiṇī's letter, which speaks Bhagavān's full majesty as well as His beauty.

• Where do you bypass legitimate gates when the proper procedure would actually work?
• How do gates honor what shortcuts miss?

The brāhmaṇa walks into Dvārakā and walks straight into the golden throne-room — like a man bringing a folded note to a king, only the king turns out to be the Original Person seated as if waiting for that very note. Gatekeepers, throne, gold — every Vedic mark of majesty is in place precisely so that the messenger can recognize whom he has reached.