Learn Finnish: Sinullahan on vihta? - You have a sauna whisk, right?

Instead of asking an open yes/no question, the -han clitic expresses an expectation. It turns the statement into something like 'You have a sauna whisk, right?' or 'I assume you have one.' It seeks confirmation rather than just asking for information.

Why is the clitic attached to sinulla and not the verb on?

The -han/-hän clitic usually attaches to the first word of the clause. Here, the speaker starts with sinulla to focus the sentence on you having the whisk, and the clitic firmly locks onto that first word.

Why is the clitic spelled as -han instead of -hän here?

This is due to vowel harmony. The clitic effectively becomes a part of the word it attaches to. Because the host word sinulla contains the back vowels u and a, the clitic must also use a back vowel, making it -han.

Is vihta the only word for a sauna whisk? I've seen another word for it.

You might be thinking of vasta! Both words mean exactly the same thing. Vihta is traditionally used in western Finland, while vasta is used in eastern Finland.