I’ve got two answers for this, one for before the apocalypse happened, and one for after.

Before the apocalypse, it’s easy enough. I wanted the tech of that era to be near-magical, so that after the apocalypse it’s seen as magical.

1- There’s already a bunch of mall santas (that profession is still around in the 2100s), just hire one.

2- Get a large sack, buy a bunch of toys off A3 (Amazon-Alphabet-Apple), done.

3- You’d have several choices for this. If you’re on a low-gravity world, you can hide propellers or thrusters inside the sleigh and it’ll probably be enough to fly. On Earth though, you’ll either need to basically build it as a massive 4-rotor drone, carry it with a helicopter, or use anti-grav tech. I’m leaning towards the former, since I haven’t decided yet how I want the pre-apocalypse anti-grav tech to be like. That’s the flying done, the sleigh shape is just building a decorative frame.

4- Humanity’s gene-editing tech isn’t good enough to make flying reindeer, so they’ll have to be regular reindeer strapped to a rig in front of the sleigh. It might be hard to make that look convincing.

5- Humanity’s gene-editing tech is good enough however, to make a reindeer with a florescent nose.

As for difficulty, the hardest part here would be getting permission to modify a reindeer to have a glowing nose. The rest is doable for a small dedicated group.

If they actually try to break into houses though, they’ll just get arrested. That is if they don’t get shot down first for refusing to identify themselves (“Santa” is not a valid identification number) and going into controlled airspace.

After the apocalypse, it becomes significantly more difficult, for obvious reasons. Note, the post-apocalyptic part takes place on a far-off moon called Eren B, with about 1/3rd Earth gravity and few Earth animals.

1- Finding someone fat might be difficult, as the low gravity kinda stretches everyone out vertically, but it’s definitely doable. The beard and red clothes is easy.

2- Easy, sacks are everywhere. Obtaining that many toys would be expensive but that’s nothing compared to the next few points.

3- Oh boy, this would be almost impossible. You can “fly” using a Shard Of Gravitation, but the problem is that you only have control over how strong it is, which is why they are primarily used to lighten vehicles instead of fully lifting them off the ground- if you lift off, you have 0 control. There have been experiments with people strapping 5 or 9 Shards to a single platform, with them arranged around the sides, so by changing their strength you can stay upright, but that is insanely expensive- even a single shard is worth more than some villages. And it still only lets you hover, not control your movement. Perhaps, if you manage to find an undamaged fully functional ancient sky-ship (an artefact that would quite possibly be the most valuable thing on the planet), and built a wooden frame around it, you could get a flying sleigh. I suppose another way would be to invent airships. Eren B’s low gravity make them a lot easier to build, but that would still require a bunch of technology that just isn’t available to them.

4- Impossible again. Reindeer don’t exist on Eren B. The original terraforming effort didn’t move over the entirety of Earth’s ecological diversity, as that would have been pointless. Reindeer were left behind, together with most of the substitutes you could use. The closest you could get would be to strap horns to a horse, but that’s still difficult, as there are very few horses on Eren B and the ones that are around are carefully guarded by a (currently unnamed) group in the south, because of the large advantage it gives them. It’s not entirely impossible to get a couple from them though, either through trade or by stealing them.

5- I guess you could strap a lantern to a horse’s nose? You’re already strapping horns to them.

This would be impossibly difficult. No.3 especially is the issue, even if the entire planet was dedicated towards this goal that would still probably be impossible.