Learn Dutch: Velen zonderen zich af van de menigte. - Many isolate themselves from the crowd.

Because it acts as an independent noun referring to people. When words like vele, sommige, or andere stand on their own without a noun right after them, you must add an -n if they refer to human beings. If it were followed by a noun, it would just be vele mensen.

Why is af separated from zonderen, and why is zich in between?

The infinitive is zich afzonderen (to isolate oneself). It is a separable verb, so the prefix af moves later in the sentence. The reflexive pronoun zich immediately follows the conjugated verb zonderen, giving us zonderen zich af.

Can I use veel instead of velen to mean 'many' here?

Not as an independent subject referring to people. Veel is generally used for uncountable nouns (like 'much') or as an adverb. To say 'many people' in one word, you need the inflected plural form velen.

What is the root of the verb afzonderen?

It comes from the word zonder (without). By adding the prefix af-, it becomes a separable verb meaning to put someone or something apart, or literally 'without' the rest of the group.