It’s kind of odd that it doesn’t matter for a single human whether they die from sudden car accident or get obliterated by supernova. Both events feel equal

The "heat" IS the radiation. So, yes.

Someone correct me if I'm missing some nuance here, but heat doesn't get transferred directly through space because heat is vibrating molecules and space is a vacuum. The sun radiates (speed O' light). A lot of that radiation just reflects off the earth (or we wouldn't be able to see it), but a lot of it gets absorbed. THAT's when it's converted into heat energy. It's also why the greenhouse effect is a global phenomena: light energy comes in across the vacuum relatively easily, turns to heat on Earth instead of being reflected, heat energy cannot escape as easily as light energy.

When there is a total solar eclipse, the temperature does drop dramatically. But it might not be detectable on the other side right away for sure.

Yes, we have conduction, convection, and radiative heat transfer. Vacuum insulates the first two, it's the light from the sun that heats us up

It wouldn’t really be faster than normal nighttime cooling. However, that cooling would continue instead of having the sun to start warming stuff up in the morning.

Equal to speed of light in vacuum

https://en.m.wikipedia.org/wiki/Speed_of_gravity

light speed = gravity speed

From an AI, so take with some salt:

Yes, gravity is believed to travel at the speed of light.

According to Einstein's theory of general relativity, the effects of gravity propagate through spacetime at the speed of light. This means that if a massive object were to suddenly change its position, the gravitational effects would not be felt instantaneously by objects around it, but would instead spread outward at the speed of light.

This is in contrast to the classical Newtonian view of gravity, which treated it as an instantaneous force. Einstein's theory showed that gravity, like other forms of electromagnetic radiation, obeys the speed limit set by the speed of light.

Experimental evidence, such as observations of binary pulsars, has confirmed that gravity does indeed propagate at the speed of light, as predicted by general relativity. This is a crucial aspect of our modern understanding of the nature of gravity and its relationship to the fabric of spacetime.​​​​​​​​​​​​​​​​

Gravitysimulator.org has an interface you can simulate what happens, though it's timeframe is on the order of days. Not seconds.

Why would it travel radially away? The resulting gravity wave from a disappearing stun much push the Earth a little, but changing its orbit that drastically would mostly destroy Earth anyway.

I think that's just the wording. My interpretation of that is any satellite or space probe sending back readings to Earth wouldn't be faster than the sun visually disappearing from the sky. Even with the information being transmitted at the speed of light, there's always going to be some sort of processing delay, along with the limited bandwidth of the transmission.