Yes, Popeye will eat his spinach and rescue her.

Nope. Nothing oily that doesn’t rinse away completely with water. Most people forget butter and peanut butter, too.

I’m pretty sure the risk is lower, but you probably still shouldn’t. I think the problem is that anything fatty/oily can emulsify with other things that get poured down the drain and potentially thicken into a blockage even if they weren’t in that state when you poured them down