1. The ball under the desk are some.

(Is this correct?)

2. When is your birthday?
2-1. It is January 25th.
2-2. It is on January 25th.
2-3. My birthday is on January 25th.
2-4. My birthday is January 25th.
(Which answer is correct? Are all correct?)

#1 makes no sense at all. First, ball is singular, are is plural and some is plural.

All of #2 are correct

Thank you. Then, what about the following?

The balls under the desk are some.

(Is it correct? If not what expressions do we have to use?)

Yes, that is far far better! However what do you mean by "some?"

Sra

1. The sentence "The ball under the desk are some" is not grammatically correct. It should be revised to "There are some balls under the desk" or "Some balls are under the desk."

2. In response to the question "When is your birthday?" the following answers are grammatically correct:

2-1. "It is January 25th."
2-2. "It is on January 25th."
2-3. "My birthday is on January 25th."
2-4. "My birthday is January 25th."

All of these answers convey the same information and are considered grammatically correct. The choice of wording may vary depending on personal preference or context, but they all convey the same meaning.