1. I got a nice gift which is for my birthday.

2. I got a nice gift for my birthday.
(Can we use #1? In #1, "which is for my birthday" is an adjective clause. In #2, doesn't 'for my birthday' modify 'gift'? Isn't it an adjective phrase?)

3. I'm looking for a present which is for my daughter's birthday.

4. I'm looking for a present for my daughter's birthday.
(Can we use #3? In #1, "which is for my daughter's birthday" is an adjective clause. In #4, doesn't 'for my daughter's birthday' modify 'present'? Isn't it an adjective phrase?)

The use of the adjective clause, "which is..." is not wrong, but it's cumbersome and awkward. Use of the prepositional/adjective phrase is enough. It would be even simpler to merely say, "I'm looking for a birthday present for my daughter" or "I got a nice birthday gift."

In both sentences 1 and 2, "which is for my birthday" is a relative clause that modifies the noun "gift". However, there is a slight difference in the usage of "which" and "for my birthday" in these sentences.

In sentence 1, "which is for my birthday" provides additional information about the gift, specifying that it is intended for the speaker's birthday. This relative clause can be preceded or followed by a comma, depending on the writer's preference.

Example: "I got a nice gift, which is for my birthday." or "I got a nice gift which is for my birthday."

In sentence 2, "for my birthday" acts as an adjective phrase that modifies the noun "gift". It specifies the purpose of the gift, indicating that it is intended for the speaker's birthday. No comma is necessary in this sentence.

Now let's move on to sentences 3 and 4. Similarly, "which is for my daughter's birthday" in sentence 3 is a relative clause that modifies the noun "present", indicating that it is intended for the speaker's daughter's birthday. The relative clause can be preceded or followed by a comma.

Example: "I'm looking for a present, which is for my daughter's birthday." or "I'm looking for a present which is for my daughter's birthday."

In sentence 4, "for my daughter's birthday" functions as an adjective phrase that modifies the noun "present", specifying the purpose of the present. Again, no comma is necessary.

To summarize, both sentences 1 and 3 can be used, with the relative clause providing additional information about the noun it modifies. Sentences 2 and 4 can also be used, with the adjective phrase specifying the purpose of the noun. It depends on your preference and the stylistic choice you want to make.