1) Can you chain these as an ongoing string? If so, what's the limit?
2) Are these wall-powered? Hard to tell for sure from the pictures how these are actually powered
3) If my phone isn't there anymore (after they've already been configured for lighting), will they continue or do they need the ongoing BT connection to work right?
Tanios1) If you look really close, you can see the 12V waterproof connector on the left side of the picture. That's a standard outdoor 12V connector. From what I can see it comes with a 12V AC adapter (probably not waterproof, so you'll have to protect that from the weather, or tie into a 12V outdoor lighting transformer), and you will need to respect the output of the adapter. I think I saw each lamp uses 3Watts.
2) Yes they are wall powered (but you probably gathered that from the answer to #1.
3) @nullghost had the right idea. Typically these things remember how you set them last time and will run that way when the power is turned on. It isn't clear from what I can find.
Taniosi think it is expandable due to the connections and the some description on amazon that this company has the additional 3pcs expandable strings sold on amazon