If I return a faulty product and the retailer does not agree to give me a refund but does offer a brand new replacement product, can I then return that new product for a refund?
No. You are entitled to a replacement, repair or refund but it's not your choice and they're not interchangeable.
Yes, but if the replacement is unopened and returned in a saleable condition, am I not entitled to a refund on that then?
Nope, you're never automatically entitled to a refund no matter the condition of the item. The place might have a policy to take back unopened items but if not, you can try the SCC to push for your chosen resolution but there's no guarantee you'd win in such a case.
You've no legal right to return any unopened product for a refund (except if it was sold online, where you've 14 days).
Some stores do have such a policy, but that's part of the sale contract. There is no general legal right to return unopened goods for a refund.