No they don't

They are closed on Sundays.

Inter-island only

I don't believe so. It's phone orders or in person. The mochi have a short shelf life, like two days if they contain fresh fruit

Yes, you should keep them cold, but they only stay at peak freshness for a day or two. Still good after that, but the berries are very ripe and perfect for eating when you get them.

No

I doubt they ship

I doubt they do that, but you could ask.