Translation:Most of my cousins live in Finland.
Yes, absolutely. Like det, you could pronounce it the way it ought to by appearance, but it would sound very formal. It's something I would expect at, say, a Nobel prize recognition ceremony.
That's just not English. We say "Most of my..." or "The majority of my...". You can't mix them.
Because "flest av" is simply not correct. There are many situations where you cannot translate word for word between Swedish and English, and this is one.
I'm finding many uses of "de flesta [noun]", without the "av". Is it optional, or is it required in this particular construction?
I discovered this source, but it makes "de flesta" seem very complicated... https://books.google.com/books?id=Zu6ykpApmdMC&pg=PA213&lpg=PA213&dq=swedish+de+flesta&source=bl&ots=wAdRXHdPOp&sig=zqsbaTEkpH8aTsYQ9zxtzEcwbaY&hl=en&sa=X&ved=2ahUKEwjh77DFmfjcAhVn44MKHck1BEMQ6AEwBnoECAQQAQ#v=onepage&q=swedish%20de%20flesta&f=false