1. He felt happy.

2. He felt happiness.
3. He felt sad.
4. He felt sadness.

(Are they all grammatical?)

Yes, all are grammatical. #s 1 and 3 are most commonly used, but they are all correctly written.

They're all correct -- but 1 and 3 are used most often.

Yes, all of the sentences are grammatically correct. They use different forms of the verb "feel" and convey different emotions by using either the adjective form (happy, sad) or the noun form (happiness, sadness).

Yes, all four sentences are grammatically correct. However, each sentence conveys a different nuance.

1. "He felt happy." - This sentence describes the emotion of happiness that the person experienced.
2. "He felt happiness." - This sentence emphasizes that the person experienced the specific feeling of happiness.
3. "He felt sad." - This sentence describes the emotion of sadness that the person experienced.
4. "He felt sadness." - This sentence emphasizes that the person experienced the specific feeling of sadness.

In general, "happy" and "sad" are adjectives that describe the person's emotional state, while "happiness" and "sadness" are nouns that refer to the emotions themselves. Both forms are grammatically correct, but the choice depends on whether you want to describe the emotion itself or the person's experience of that emotion.