The issue there is that if we are capable of doing something it is hard to say whether or not it is part of our determined nature. For example, maybe we have an evolutionary adaption to famine where elderly people are biologically tweaked to be OK with starving themselves to death. That'd be pretty gruesome and I doubt they'd be excited at the prospect even if a mechanism does exist, but it is the sort of thing that evolution is perfectly capable of encoding into us.
It is less direct to the examples you give; but I'm confident that parents are psychologically designed to sacrifice themselves in the event it helps their children and many men, famously, are built to go to the frontlines and sacrifice themselves for family and community. Hard to make an assessment of whether those sort of choices is free will or determined nature.
Right. But free will is anti-deterministic, instead of undeterministic. That's why the "free" part gets confusing, because we are always limited, and yet free will is an intelligence power. Parrots can't lie, they reproduce sounds, humans can lie and encode lies as sounds. LLM's don't currently lie, since lying is strategic. Free will is about strategically choosing actions. Free will doesn't tell us anything about the (non)deterministic nature of the universe or ourselves.