Standard limited power landscape cable should do the job in most cases.
You can find dual listed LV and CL2 product that can also be run in walls and chases.
Nope. Anyplace that deals Southwire should give you some choices, but there are lots of other manufacturers. Or you can get landscape wire at any of the big home improvement stores. Typically 2-wire #16 and larger (zip cord).
Intermatic Malibu LV lighting comes with an outdoor rated LV wire. One thing that's nice is that it has a rubberized insulation that you can use vampire clamps on, and when you remove them, the holes self seal. I've bought that cable in bulk before, I think it was actually made by Carol Cable, but I can't remember for sure.