Learn Arabic (Modern Standard): قرأ مقالات كثيرة في المجلة.

This is because of the non-human plural agreement rule. In Arabic, plural nouns that do not refer to humans (like objects or concepts such as مقالات) are treated grammatically as a single female. Therefore, the adjective describing them must take the feminine singular form, which is why كثير gets the feminine ة ending to become كثيرة.

Where is the word for 'he' in this sentence?

The 'he' is built directly into the verb قرأ. This is the basic, root form of the past tense verb. In Arabic, a past tense verb without any added suffixes always implies 'he' did the action.

How can I tell that مقالات (articles) is a plural word?

You can recognize it by the ـات suffix at the end. This is the standard regular feminine plural ending in Arabic. The singular word is مقالة. To make it plural, we drop the singular feminine ة ending and add ـات.

Why doesn't the adjective كثيرة have the definite article الـ (al-) at the beginning?

In Arabic, adjectives must match their nouns in definiteness. Because مقالات is indefinite (meaning 'articles', not 'the articles'), the adjective describing it must also be indefinite and leave off the الـ prefix.