Asklemmy

Jumping off the ISS wouldn’t cause you to de-orbit—it would just put you in a slightly more elliptical orbit that would eventually intersect the ISS again.

And if you did get into an orbit that took you down into the atmosphere, no parachute would save you—parachutes are for slowing to a safe landing speed from terminal velocity, not from orbital velocity. You’d need to go through atmosphere too thin to fill a chute, but still fast enough to burn you up.

If you just stepped outside of ISS you'll still be in an orbit around earth ( something something first law of motion) it would take you decades to loose enough energy to deorbit and if you survived that long without eating drinking shitting then good luck surviving the reentry.

The answer to this depends on how much the magic device with the oxygen weighs.

Also just going to set aside anything to do with sky diving and space suits and having friends and everything else that I don't know anything about.

I only know this from playing Simple Rockets on android but basically you direct your thrust in the direction you're moving in order to reduce your velocity, and you'll fall down to earth.

Think of an orbit as the balance between falling towards earth and zipping past earth. If you fly past too fast then you just fly past and maybe the gravity pulls you a bit but not much. If you fly past too slow the gravity pulls you down to earth and you crash. If you fly past at the same speed you fall towards earth the two directions balance out and you end up just spinning around earth.

Therefore, If you're in a stable orbit on the space station, and then you slow down, you'll start to fall down towards it instead of "falling" around it in an orbit.

If you only slow down a little bit you'll start moving towards Earth but you'll be moving way too fast for an unshielded human to enter the atmosphere without burning up.

You'd have to slow yourself down, by directing thrust towards the horizon you're headed towards, enough so that you're not going fast enough to burn up.

Whether or not you can slow down enough, quickly enough, depends on how much thrust your magic device can provide and how much that device makes you weigh.

It seems difficult to have enough bottled oxygen to deorbit yourself, but maybe doable.

The MMU backpack units on the space shuttle had a total delta v of ~30 m/s. You need about three times that amount to deorbit from ISS. So imagine you need 3 MMUs give it take worth of expendable propellant oxygen, and you can do it. (The MMUs used nitrogen, but for this purpose oxygen is pretty much the same.)

After you deorbit, you will of course burn up on re-entry with no heat shield. But it might be conceivable to design a personal heat shield surfboard.

You could also avoid the whole burning up things by braking a lot more during the deorbit maneuver. But instead of 100 m/s, you need to slow down by more than 7000 m/s. That's quite a few more MMUs worth of gas. But if you do that, then you're essentially making a free fall jump from space, which has more or less already been demonstrated.

Edit:

To address the linked article in some way: each astronaut on the station has a dedicated seat on a capsule to come back down in an emergency. Usually, it's the same space capsule you came up on, but not always. Those are maintained ready to go at all times, and the astronauts can be back on the ground in 60 minutes whenever they need to. These spacecraft can be operated to splashdown by astronauts alone with no ground assistance, if needed.

You're going much too fast to hit the earth, you'll miss it and continue in orbit. To deorbit, you'll need a lot of things to throw in the other direction, like the oxygen from your magic tank. You'd need about a full rocket full of oxygen (~170 tons) to slow down, probably more because the exit velocity would be slower than a rocket.

The other issue with this scheme is you'd slow down too slowly. You'll start getting slower and lower, but you'd start to get into the atmosphere, which because you're still going so fast would cause you to not have a great time. So your magic oxygen bottle will also need a massive tube off the end of it, maybe a couple meters in diameter.

But if you had your magic infinite air tank with a huge tube off it, theoretically you could get back down to earth safely with just it, a space suit, and a parachute.

…what??? What does that have to do with the link? You would die in atmosphere.