1. I like an apple. (one)

2. I like pears. (generic use)
3. I like a drama club. (generic use)
4. I go to a sports club. (one)
5. A dog is a faithful animal. (generic use[front]/ one [back])
6. I like going to a soccer club.(one)
7. We have a baseball club and two soccer clubs. (one, two)

(Are my explanations correct? the use of 'a' and 'plural nouns')

They seem correct to me! =)

Your explanations are mostly correct regarding the use of "a" and "plural nouns". Here is a breakdown of each sentence:

1. I like an apple. (one)
Explanation: In this sentence, "a" is used to indicate a single apple that you like.

2. I like pears. (generic use)
Explanation: In this sentence, the use of plural form "pears" suggests a general liking for pears in general, rather than a specific quantity.

3. I like a drama club. (generic use)
Explanation: Here, "a" is used to indicate that you like the concept of drama clubs in general. It implies that you have a fondness for any drama club, not necessarily a specific one.

4. I go to a sports club. (one)
Explanation: Just like in the previous sentences, "a" is used to indicate a single sports club that you go to.

5. A dog is a faithful animal. (generic use [front] / one [back])
Explanation: In the first part of the sentence, "a" is used to show that a dog, in general, is a faithful animal. However, in the latter part of the sentence, "one" is used to refer to a specific animal, confirming that the statement also applies to a particular dog.

6. I like going to a soccer club. (one)
Explanation: Similar to the previous sentences, "a" is used here to indicate a single soccer club that you enjoy going to.

7. We have a baseball club and two soccer clubs. (one, two)
Explanation: In this sentence, "a" is used to refer to a single baseball club that you have, while "two" indicates the quantity of soccer clubs that you possess.