Are propane lanterns safe to use indoors during power outages?

Yes, with a caveat. There are propane and natural gas stoves in use in houses throughout the world, and as with a gas kitchen stove, a small propane lamp will not normally produce CO. However, if you are in an unventilated room, eventually you will use some of the O2 up when there is flame present. When the O2 level begins to fall, the likelihood of producing CO will rise. So, ventilation is important, just as if you were cooking with gas. Just as with everything, as long as you use your head, a propane lamp is an excellent emergency preparedness tool- it supplies light, and heat, plus a comfort factor.

Depends on what you mean by indoors. If your house? You'll be just fine, in a tent? make sure you have plenty of ventilation. I wouldn't use it in a sealed tent in the rain (a rain soaked tent DOES NOT BREATH). But on a nice night with a mesh tent or with the panels unzipped you would be fine with this lantern.

Absolutely not. Depending on how much oxygen is present, it'll produce water vapor, carbon monoxide, carbon dioxide, and straight carbon (smoke). Most of things will kill you in a confined space. Get an LED lantern (Black Diamond Apollo, Brunton Polaris, Glorb, or Orion) or some emergency headlamps (Petzl e+LITE).