• vārṣikān — of the rainy season
  From varṣa (rain). Cāturmāsya — the four months when sannyāsīs traditionally do not travel. The cosmic schedule provides the cover; the līlā uses dharma's own clock to bring devotees together.
• sva-artha-sādhakaḥ — trying to achieve his own purpose
  Compound: sva (own) + artha (purpose) + sādhakaḥ (one accomplishing). Bhāgavata-kavi names Arjuna's purpose 'sva-artha' without irony — because his sva-artha is woven into Kṛṣṇa's saṅkalpa, it is legitimate, even sacred.
• rāmeṇa — by Lord Balarāma
  Instrumental of Rāma — here Balarāma. Gauḍīyas mark how Balarāma honors Arjuna without recognition: the disguise works because Balarāma operates in the mood of guru-bhāva toward sādhus, not investigative scrutiny.
• ajānatā — who was unaware
  Present participle of √jñā with negative. The all-knowing Balarāma chooses not to know — this is yogamāyā, the līlā-śakti that veils omniscience so the story may unfold. Bhagavān's not-knowing is volitional, not deficient.

• What outcome am I rushing that needs me to stay through a monsoon first?
• Where could waiting through difficulty actually be the action?

The monsoon keeps the wandering yogi in one place — the rains are Kṛṣṇa's own way of arranging that Arjuna stay until Subhadrā appears. Even the weather is Kṛṣṇa's confidant in this saṅkalpa.