It ought to be me rather than you that sign the letter.

sitifanWhat's the difference in meaning

No difference. It's two different ways to say the same thing. There are many ways to say it.
I think I would usually say,
I should sign the letter -- not you.
I should be the one to sign the letter -- not you.
CJ

He is an artist rather than a politician.
What does the above sentence mean, A or B?
(A) He is an artist, not a politician.
(B) He is more an artist than a politician.

I would interpret it as (A). "rather than" is often used to correct the false ideas of others. It often takes on the meaning of "instead of".

-- He is one of Julia's brothers.
-- No. He is a cousin rather than a brother.
But truth be told, this is not a much used pattern for "rather than". It's more common for "rather than" to be used before verbs.
Rather than arguing

CalifJimBut truth be told, this is not a much used pattern for "rather than". It's more common for "rather than" to be used before verbs.

Does "truth be told" mean "to tell the truth"?

1. The teacher rather than the students ____ to blame.
(A) is (B) are
2. It ought to be me rather than you that ___ the letter.
(A) signs (B) sign
3. It ought to be you rather than me that ___ the letter.
(A) signs (B) sign


What are the correct options to the above questions?

The given answers are ABA. My choices are AAB.

sitifanDoes "truth be told" mean "to tell the truth"?

Yes. It's an alternate wording for that idiom.
CJ

sitifanWhat are the correct options to the above questions?

If I'm not mistaken, the rule for "rather than" says to make number agreement in the third person with the noun that precedes "rather than".
But I may be mistaken, so I can therefore only tell you how I would answer -- not what is truly "correct" from the viewpoint of the test maker.
1.

CalifJim3. A - signs (you -- singular --signs)

I could be wrong, though, so hopefully, someone else can confirm or deny.

YOU is always plural, isn't it?

sitifanYOU is always plural, isn't it?

Yes, grammatically. But the reference of "you" can be one person or more than one.
Even though I say "You are smart" I'm only talking to one person.
And in this "rather than" structure, it seems to me that the agreement is made with the number of the reference only.
If you means more than one,

.
I think it should be AAA. As a quasi-coordinator, rather than often works like a phrasal preposition:

1. Rather than the students, the teacher is to blame.
2. Rather than you, it ought to be me that (who) signs the letter.
3. Rather than me, it ought to be you that (who) signs the letter.
.