Learn Spanish (Latin America): Los estudiantes tienen muchas preguntas.

We use a form of mucho (a lot / many) with nouns, and it has to match the noun's gender and number. Since preguntas (questions) is feminine and plural, we use muchas. We only use muy (very) to describe adjectives or adverbs, not objects.

Why does the verb tienen not have que after it here?

The verb tener on its own means to possess something, so tienen means "they have". You only add que when you want to say someone "has to" do an action, like in the phrase tienen que estudiar (they have to study).

Is the word estudiantes masculine since it uses los?

The noun estudiante is used for both genders: el estudiante (male) and la estudiante (female). In the plural, los estudiantes refers to a group of male students or a mixed group of male and female students.

If preguntas means "questions", how do you say "to ask"?

The verb for "to ask a question" is preguntar. In Spanish, it is very common for nouns and verbs to share the same root word, which makes them easier to remember!