First case:
A normal product lookup would look like this
http://our.api.com/product/1
So Im thinking that best practice would be for you to do this
http://our.api.com/Product/101404,7267261
Second Case
Search with querystring parameters - fine like this. I would be tempted to combine terms with AND and OR instead of using []
.
PS This can be subjective, so do what you feel comfortable with.
The reason for putting the data in the url is so the link can pasted on a site/ shared between users. If this isnt an issue, by all means use a JSON/ POST instead.
EDIT: On reflection I think this approach suits an entity with a compound key, but not a query for multiple entities.