No.
As far as I know browning did not have any firearms made for them in australia.
Not a one. FN made firearms for Browning.
Browning never made firearms in Ohio.
Browning has parts made in numerous factories. Belgium, Portugal, Japan to name a few.
Contact Browning Firearms Customer Service through their website.
John Moses Browning
John Moses Browning
They have been made in several nations- Belgium, Portugal, Canada, Japan, and the US.
Browning made .22 rifles AND pistols- you did not tell us what you have. The Browning website, customer service, has historical data for many Browning firearms by serial number. See if your model is listed. If not email Browning.
There were two companies known as Interarms. The first was an importer/exporter, formed in 1953. They did not manufacture firearms. The second - and current - Interarms is a subsidiary of Hi Standard, and does not manufacture a PPK or PPK/S pistol. If what you have is actually a Walther PPK/S, value could range anywhere from $300 - $800, depending on specifics.
John Browning was an American firearms designer who developed many varieties of firearms, cartridges, and gun mechanisms.