Why is it van and not vannak? It is more the one tourist that is in the water so shouldn't the 3rd person plural be used?
No because the verb "van" have to correspond with the noun "turista", and in Hungarian you use singular after "sok" sok turista, but NOT sok turisták (the same for numbers like öt turista, NOT öt turisták). And if the noun is in singular, then the verb have to be too.
Hungarian language uses the singular for the word Sok:
(remember the last lesson with Numbers)
Engl. five students
Hung. öt diák
Rather than using the plural, diákok, we use the singular after number words in Hungarian: diák.
Accordingly, the verb in Hungarian also shows the third person singular form, rather than the plural. Compare: