Why is it hafte and not hafta?
The में makes it oblique.
Why hote hai and not just hai?
Sentences which convey an univeral truth will have to end like that
eg. एक साल में बारह महीने होते है
Isn't just हफ़्ते में सात दिन होते हैं। ok as well?
Correct.
Could it also be arranged as "सात दिन एक हफ़्ते में होते हैं" ?
Can ,,ek saptah mein saat din hote hain,, also be used?
Yes. सप्ताह and हफ़्ता are synonyms. Just that one comes from Sanskrit and the other from Persian. You can report if it is not accepted.