1) It is presumed that you are talking about Delivery challan. A Delivery Note or challan is a document addressed to the Stores -in-charge containing instructions to effect delivery of the goods mentioned therein. A copy will go along with the goods package to the customer.
Invoice is a document to raise demand on a customer ( usually in case of credit sales), for the goods supplied to the customer. Based on a copy of the invoice, the concerned customer account will be debited for the sales made. It is also called Credit Bill, taking it as a document representing a demand for a credit sale. Some people call it a Debit Bill, taking it as a document, based on which a debit is made in a customer account.
Bill is a document representing a cash sale. It is also called Cash bill. No debit is raised.It is closed by a 'Cash Received' stamp on it.
2) Since it is a credit sale, a demand should be raised on the customer, by preparing an Invoice/Debit Bill/Note, irrespective of whether the customer wants it or not. Based on this only, a sale is recognised (even though money is not received) and the customer account is debited in the ledger.
3) A sale is defined as transfer of tilte to goods for a consideration (Price). General understanding is that the ownership in goods, passes on to the buyer at the time of delivery and therefore, sale should be recognised at the time of delivery of goods by preparing an Invoice or a Debit Bill/Note. The document prepared should be serially numbered in the order of deliveries made. No such situation as mentioned in the question should arise.