Hi jhenry
The short answer is - don't ever void a check unless reversing is not an option. Voiding an issued check is essentially no different than clearing that check; there is no GL effect and the vendor history looks like the check was issued. A void check in Adagio is one which you attempted to print unsuccessfully; when the question "did the check print correctly" comes up, you answered NO.
I am not 100% sure I understand the second question, but if what you are referring to are zero balances that appear on the pre-check register, here is the answer. Those zero balances are caused by invoices and offsetting credit notes or adjustments on a vendors account which net to zero, but which don't "see" each other. To make them "see" each other, you enter a fake manual check, paying the offsetting transactions. Don't tag the "print check" box, and enter a fictitious check number, such as 999999. When you post the manual check batch the pre-check register will be rid of those transactions.
Steve