Leomund's Tiny Hut
Range: Self (10-foot-radius hemisphere)
Hemisphere: One 1/2 of a Sphere, a partial sphere. IE: Dome.
...A 10 foot radius immobile dome of force springs into existence around and above you and remains stationary...
Unfortunately the intent* of the spell is in it's very first line. It creates a half spherical dome that appears (again emphasizing the precise RAW text here to avoid interpretation arguments) around and above you but not below you that barres creatures outside of it from passing through it. Since the magical walls of this barrier specifically do not extend below the caster, then anything capable of tunneling up through the ground or passing through the ground is fair game for entering your hut from the underside.
Let's hope a Buelette doesn't wander by!
*Finally officially explained here
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.
Best Answer
The relevant part of the Leomund's Tiny Hut (PHB, 255) spell description states:
Based on that description, in order to pass out of the dome, the arrows would have had to be inside the dome initially. If they were inside the dome initially, it should be possible to shoot them back inside the dome as well.