Learn Farsi: او بیشتر اوقات مجله می‌خواند.

ouqât is an Arabic broken plural of vaqt. Instead of adding a regular Persian plural ending like -hâ, the internal vowels change and syllables are added. Persian uses many of these inherited Arabic plurals for common words, especially in set phrases like bishtar-e ouqât (most of the time).

Do I need to pronounce an Ezafe (the hidden linking vowel) between bishtar and ouqât?

Yes, it is pronounced bishtar-e ouqât. The Ezafe links the word bishtar (more/most) to the noun it quantifies, literally translating to the greater part of times.

Can I just say bishtar-e vaqt-hâ using the regular Persian plural instead?

Yes, bishtar-e vaqt-hâ is grammatically correct and perfectly understood. However, bishtar-e ouqât is a very frequent fixed expression, so learning this specific broken plural is essential for understanding native speakers.

The English translation says he reads magazines, but majalle does not have a plural ending here. Why?

In Farsi, when you refer to a general category of things or a general habit rather than specific individual items, you use the singular form. Because he is just reading magazines in general, majalle remains singular.