“2. So can the context of this phrase be used as evidence that Buddha said samadhi, not jhana, to someone who is a layperson?”
I have explained the difference between jhana and (Samma)samadhi. Let me try to summarize.
– There can be pannavimutti Arahants who have completed Samma Samadhi without cultivating jhana. King Suddhodana is probably a good example. He is said to have attained Arahanthood close to the moment of death.
– There can be cetovimutti Arahants who get to the Arahant stage via Ariya jhana. Ven. Moggalana is an example.
– Also, there can be ubhatovimutti Arahants who had not cultivated jhana, get to the Arahant stage by pannavimutti, and simultaneously receive all jhanas and iddhi powers. Culapanthaka Thero is a good example here.
– There can be anariyas who had cultivated all four rupavacara jhanas AND the four arupavacara samapatti. They are NOT released from the apayas in future lives. However, they will be born in a Brahma realm at death. Alara Kalama and Uddaka Ramaputta are two good examples.
Samadhi and jhana are two different things.
– There can be miccha samadhi, too, as I explained above.
– In that particular sutta (Potaliya Sutta), the Buddha refers to those who attained Ariya jhana. We can say that they have both Samma Samadhi and Ariya jhana.
– But there can be Arahants who completed Samma samadhi but have not cultivated the four jhanas. But they may get to at least the first jhana at the moment of Arahanthood.
– Magga phala do not necessarily involve jhana. The sequence of getting to magga phala: Parikamma (P), Upacāra (U), Anuloma (A), Gotrabu (G), Path (magga) (Pa), and Fruit (phala) (Fr). Those are different stages of samadhi getting to the Gotrabu (change of lineage). See #14 of “Citta Vīthi – Processing of Sense Inputs”