I wonder what your thoughts are about this product.
This is grammatically correct. The ordering feels a bit off to me – I'd prefer the “are” to go at the end – but that preference feels weak enough to be just my dialect.
To answer the first question:
I wonder what your thoughts on it are.
The simplest sentence of this form is “I wonder what it is.”. I feel like it breaks down like this, though I couldn't possibly tell you why:
┌ wonder ┬─────────.
I what ┬─ is
(I wonder (what it is)).
jr_kim's answer, “I wonder what are your thoughts about this product” isn't incorrect per se, but it's a non-standard dialect; it's not formal, written English, and some might consider it a little odd. With different punctuation to make it a question with a preceding subordinate clause, however:
I wonder, what are your thoughts about this product?
it's perfectly grammatically correct.