The OP's questions are:
Does the rule (5. You use a plural count noun with no article if you
mean all or any of that thing) only apply to certain sentences?
Is that rule ok for sentences that refer to specific things such as
"He is eating apples"?
My answer: Yes, this rule only applies when talking generically in utterances such as I don't eat apples or Do you like cats?.
When you are referring to a specific subset of that item, as implied by the statement He is eating apples, then you need to apply articles rule 4 on the same webpage you link to:
You use the with count nouns ... when the listener already knows what
you are referring to.
Imagine a context in which I phone a friend and ask what her brother is doing. A reply with the definite article He is eating the apples implies that I know which apples are being referred to. For example, they are the ones I had picked from the tree in my garden and given to her the day before.
A reply without the article (He is eating apples) refers to a specific subset. But the definite article is not used because I do not have prior knowledge about the specific apples to which my friend is referring. I would be mad to infer that he is eating all the apples in the world.
Disclaimer: It was me who wrote the grammar note about articles linked to in this question. It may, therefore, be helpful to provide information about the context and audience for the advice I give in the Articles page and other grammar notes.
I wrote the page on articles as one of a series of grammar notes for my beginning and intermediate ESL learners. I wanted to give them some basic understanding without using too much off-putting terminology. Hence what resulted was simple in both language and explanation. However, I did make this explicit in the introduction to the grammar notes:
Important: The rules on these pages will help you get started in your
understanding of English grammar. Please realize, however, that
English is much more complicated than can be explained in a few simple
sentences. As you learn more, you will find examples where the simple
rules shown here do not apply. Taking note of these exceptions or
refinements will help you deepen your understanding of how English
And in the page in question about articles, I repeat this alert:
Note: This page contains short, generalized information about this
enormously complex aspect of English grammar. For more detailed
information, consult a good reference work such as Swan's Practical
English Usage. And do not worry too much about article mistakes - only
very rarely will they cause your listener or reader to misunderstand
With the above in mind, this question is probably better suited to the English Language Learners site.