1. The sun is not in "outer space" because it is big enough to have enough gravity to have an atmosphere, but more importantly...
2. The sun is not burning. It is undergoing nuclear fusion because it is so big and generates so much gravity, that the gravity actually forces elements together in the core. This resembles burning only in that it produces a hell of a lot of heat and light.

The sun isn't burning in the sense of combustion. That's when flammable things rapidly oxidize and give off light and heat. The end result of nuclear fusion looks and seems very similar but mechanically it's completely different

Simple, the Sun isn't on fire, it's a nuclear reaction.

The Sun is made up mostly of Hydrogen. Under the intense pressure the sun generates by it's own gravity, it's core is crushed into an incredibly dense and hot state.

In the core Hydrogen atoms are so close together, and move so quickly that they are able to overcome their repulsive forces (like trying to push two positive ends of a magnet together) and smash together forming a heavier element, Helium. This releases a tremendous amount of energy in the form of heat and photons (light) and is what powers the Sun.

This process is so energetic, and requires so little fuel (compared to a fire) that the Sun will keep fusing Hydrogen for Billions of years.

In larger stars this process keeps going and Helium can fuse to produce heavier elements like Oxygen, Nitrogen, Carbon, and Iron. This is where all of those elements are created. When those stars die in explosions called supernova, their enriched guts spew across the galaxy to form new planets and solar systems.

So it turns out, you are made of Star Dust

The Sun isn't "burning" in a conventional sense, but instead is going through nuclear fusion. It's a completely different process.

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The sun isn't really burning. It's so dense that it squeezes the hydrogen it's made of together into helium. This process releases some of the energy the hydrogen was carrying before it was fused, released as heat and light.

The sun doesn't burn, fire is a molecular process involving oxygen that releases energy. The sun's intense gravity forces atoms to fuse (fusion), a process that releases far more energy. That energy is then absorbed by other atoms that release the energy in photons that is picked up by your eyes.

Not directly, it takes some ludicrous number of years for the energy created at the core of the sun to actually reach the surface.

The sun is not burning the way a fire on earth burns.

It is a huge ball of plasma undergoing nuclear fusion, a process which generates incredible heat, so it burns from within due to the process, not because it is using oxygen as a fuel.

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You literally claim to have a doctorate degree and don’t understand this? How?….