hi there!!!
For the 1st sentence:
I know that the subject of a gerund form can be either in the genitive or the accusative.So, to me, both are correct.The genitive, however, is commoner. I don't know for sure if there's a clear distinction between the two and which one you should choose if "our" and "us" appeared as possible answers/distractors in the same sentence.
For the 2nd sentence:
The context would be helpful here but, generally "from" looks more appropriate: order sth from sb/somewhere.e.g. order sth from the Net.
If the speaker wanted to say that s/he was with sb else when s/he ordered the product, s/he would simply say:
We ordered the product.
Hope I've been of some help>>>