yes it's called degenerated geometry you basically create a face that has twice the same vertex, ie a edge of zero length, that will result into a "non visible" triangle. because it doesnt generate any pixels, it's a pretty good trick to keep a strip running on some other place. However not all platforms might support it…
no, the batching is only done when your material changes that is : shader or texture. then you need a new drawcall, the more drawcalls the worst. batching is good as it collects everything that has teh same "appearance" and therfore can be rendered in a single call. I refer to OpenGL here, but I assume DX wont be…