It’s likely the leading zero is to make a UPC-A (12 digits) compliant with EAN-13
The most commonly used EAN standard is the thirteen-digit EAN-13, a superset of the original 12-digit Universal Product Code (UPC-A)
The product_code field is at the top level (not nested under openfda), so only the second query would be correct. Also, the value should be capitalized: DXN.
This query will produce results you need: https://api.fda.gov/device/510k.json?search=product_code:DXN
There is only one record in this dataset that matches the criteria you provided, and since you are using the skip parameter with a value of 100, the record essentially gets excluded from the result set. Try dropping the skip parameter: https://api.fda.gov/food/enforcement.json?search=city:"Westminster"+AND+termination_date:[2011-01-01+TO+2014-01-01]&...