Spells will specify if they stop or somehow don't have an effect when you are unconscious. Spiritual weapon makes no such mention, so it hangs around doing nothing while you are out.

Summoned creatures for example all say:

disappears when it drops to 0 hit points or when the spell ends.

And all such spells have the concentration mechanic on them. There are no "general rules" to spells. (Save those mentioned in chapter 10) Each spell has it's own rules, outside of the "Spellcasting rules" of chapter 10.

For spiritual weapon the only rule for when the weapon is dismissed is:

lasts for the duration of the spell, or until you cast this spell again.

So, first up, let's define exactly what triggers Feather Fall:

1 reaction, which you take when you or a creature within 60 feet of you falls

Situation 1: You can't cast Feather Fall as a reaction to being hit - it's a reaction to falling. If damage caused you to go unconscious, causing you to fall, then you can't use Feather Fall. That's because when you're unconscious, then you're incapacitated, which means you can't use reactions.

Situation 2: Yep, that's exactly how it works. If you land before the spell ends, you take no damage, and you can land on your feet. Taking no damage doesn't depend on landing on your feet, and while the spell gives you the option to land on your feet, while ever you're unconscious, you're prone.

Situation 3: Again, to establish a baseline, the rules on falling:

If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls, unless it has the ability to hover or it is being held aloft by magic, such as by the fly spell.

There's no suggestion of a delay there, so you start falling as soon as you're knocked unconscious. However, we really have no idea how long a fall lasts. You'll have to talk to your DM about that.

Finally, there's the question of whether someone can cast Feather Fall on you when you fall into their range. The reaction for Feather Fall can only be taken when a creature within 60 feet falls, but whether "falls" means "begins falling" or "is falling" isn't particularly clear. I think most people would allow casting Feather Fall on someone falling within 60 feet even if you weren't within 60 feet of them when they started falling, but you'll need to check that one with your DM too.

All that aside, you might be interested to know about the Ring of Feather Fall - it's a magic item that is pretty much designed for this sort of situation. If you can get your hands on one, you never need to worry about falling again.