Case $1$: A Chinese Company A offered to an Australian Company B$,$ selling them a batch of some goods. Besides some necessary transaction terms and conditions were set out clearly in the offer, the offer also indicated that the payment was made by sight $\frac{L}{C}$ and the delivery was to be made within two months after receipt of the L$/$C$.$ Company B replied in their letter that they could accept the offer, but asked for immediate delivery. However, Company A didn't give any answer to this letter. Then presently Company B opened the letter of credit at sight, and indicated "immediate shipment". During that time the marketing price for the goods was rising greatly. So Company A refused to deliver the goods.

Question:

$(1)$ Was the sales contract established between two companies?

$(2)$ Did Company A have the right to refuse to deliver the goods?