1
a. They have a personality who loves to help people in need.
b. They have personalities who love to help people in need.

(Jane has a personality who loves to help people in need.
Jess has a personality who loves to help people in need.)

2
a. They will wear a dress for this party.
b. They will wear dresses for this party.

(Jane will wear a dress. Jess will wear a dress.)

3
a. They have a sister.
b. They have sisters.

(Jane has one sister. Jess has one sister.)

Which is correct, a or b?

Question

1
a. They have a personality who loves to help people in need.
b. They have personalities who love to help people in need.

(Jane has a personality who loves to help people in need.
Jess has a personality who loves to help people in need.)

2
a. They will wear a dress for this party.
b. They will wear dresses for this party.

(Jane will wear a dress. Jess will wear a dress.)

3
a. They have a sister.
b. They have sisters.

(Jane has one sister. Jess has one sister.)

Which is correct, a or b?

Answer

1. If you are a mathematician, you should choose (b).  For the rest of us, (a) and (b) are both fine, but you need to change "who" to "that".

2. (a) and (b) equally good.  Jane and Jess are wearing a dress.  (Great rhyme!). Again, mathematicians should choose (b).

3.  Both sentences confuse me.  If you tell me "Jane and Jess have sisters", I would not be sure exactly what it means.  It could even mean that Jane has two sisters and Jess has none.  To be clear, you would have to say "Jane and Jess each has a sister."

Beware, that in currentl lingo "they" sometimes refers to a single person.  I don't like it, but that's the way it is.

Answer

In all cases, b is correct.
By the way, in your first set of examples you can't use 'who' because the relative pronoun represents 'personality' or 'personalities'. A personality is not a person.