What exactly does this skill do in Daggerfall? According UESP, it causes "withering, often fatal, additional damage." How does one tell when it goes into effect?

You'll get a message "Critical Strike!" when it happens. Each time you hit someone you have a chance of it going critical. A higher skill makes it happen more often, but I don't know the exact formula.

I always take critical strike as a primary skill if my character is a thief, it's hard to last up against hard enemies if you have to poke too much with a dagger. Then again if you set your luck insanely high in the character creation, I've started the game with two ebony daggers as a thief and never needed to hunt for a weapon.

I'm a big fan of daggers, actually.

They look awesome (all other blades look the same during combat)
And they're fast. I'm like a whirlwind of death.

Of course, they break easy. But they're so light you can carry backups.

Starting luck affects your beginning weapons?

Unsure whether luck affects starting equipment.
There is a bug allowing 2 (or more) ebony daggers.
From memory it goes like this:
Create a custom character, answer the questions afterwards, at the end of character creation click reset/restart the character.
Answer the questions again, making sure you say yes to the Ebony Dagger reward both times.
Hey presto, when you start the game you will have two daggers.

Although it has been a while and I never exploited that particular bug (one dagger was enough for me)