Translation of 'I was the one who did it'

Question

What's the correct way to translate 'I was the one who did it'? By a literal translation it would be:

Yo fui el que lo hizo.

However, I know in Spanish the verb is often made to agree with the subject, even in slightly more 'convoluted' sentences:

La persona más importante soy yo.

Does this apply to my example as well? Which is correct:

Yo fui el que lo hizo.

OR

Yo fui el que lo hice.

I think this would apply to many similar sentences of a similar form as well:

Tu fuiste el que abriste la puerta

OR

Tu fuiste el que abrió la puerta

Which of these is the proper translation?

Answer 1

This sentence:

Yo fui el que lo hizo.

it can be rewritten to:

Yo fui la persona que lo hizo.

or (this sentence sounds more natural):

Yo fui quien lo hizo.

Using la persona, Yo fui la persona que lo hice sounds wrong, "la persona" and "(yo) hice" doesn't match.

Edit: Replacing "el" por "la persona" in your last sentences:

Tú fuiste la persona que abriste la puerta. Wrong, "la persona" and "(tú) abriste" doesn't match.

Tú fuiste la persona que abrió la puerta. [OK] So your last sentence is the correct one.

Answer 2

If you want to make it sound more natural, I'd suggest something like:

Fui yo. Yo lo hice.

Answer 3

I'm not a native speaker so I'm not sure:

For the question:

¿¡Quién ha sido?!

The reply would be:

¡He sido yo!

Answer 4

If you want to use the third person, the correct way is:

Yo soy aquél ( I'm that one)

Yo soy aquél (I'm that one)
Que cada noche te persigue (Who chases after you every night)
Yo soy aquél (I'm that one)
Que por quererte ya no vive (Who doesn't live anymore because he loves you) . . .

And please note that Raphael is NOT my favorite "poet".

Answer 5

The most basic form (non-poetic) I would use is:

Fui yo que lo hice.

You use the first person to maintain agreement, similar to how whenever someone talks about seres humanos they invariably use nosotros to include themselves in the statement.