Can I see who changed a product and what they changed?

Yes. Every product has a Product Log.

1. Open the product from Products → Manage Products.
2. Click Product Log in the tabs at the top of the product.

The log lists activity for this product, newest first, with When, Admin, Action and Status. Click View on an edit to see the field-level detail: each Field that changed, with its From and To values.

Only edits made in the admin panel are recorded. If nothing has been recorded for the product yet, the page says so.