If you split your query into four parts using UNION ALL, then the order is at your leisure:
SELECT 1 AS Idx, ICAO_Ident AS ID, Location_Identifier AS LocID, Official_Facility_Name AS Name, Landing_Facility_Type AS AptType, Associated_State_Post_Office_Code AS State, Associated_City_Name AS City FROM APT WHERE `Location_Identifier` LIKE '%$fix%'
SELECT 2 AS Idx, ICAO_Ident AS ID, Location_Identifier AS LocID, Official_Facility_Name AS Name, Landing_Facility_Type AS AptType, Associated_State_Post_Office_Code AS State, Associated_City_Name AS City FROM APT WHERE `ICAO_Ident` LIKE '%$fix%'
ORDER BY Idx, ICAO_Ident
Is conn perhaps a global variable? When you are trying to access the same variable over multiple threads, such errors are bound to happen. It would be more straightforward for every thread to have it's own connection.
It depends on what you have. In some cases, redirecting to a different page after the form post can prevent the issue, because they would be refreshing the page to which they were redirected.
But if you go back with the browser, then that can be circumvented as well. In that case, storing a session token can help. After you post, store a token. If you refresh and the token is set, do nothing. When you access a certain page, you can clear the token if you want.
Posting through AJAX might be an option too, because refreshing the page wouldn't trigger the event, only clicking a button would.
You can use the mysql.exe command line tool, download mysql workbench or any third party tool to administer your database. Personally I'm a fan of Navicat, but it isn't free. IIRC Toad is a respected free tool.
MySQL server is the database part that stores the information and lets you retrieve it. The MySQL client library is the interface between your program and the server, making it easy for you to communicate with the MySQL server.
WAMP/LAMP installations come with both, a MySQL server version and the client library needed to communicate with it. What is different is that you need the .NET client library to be used with your VB.NET application, the (W/L)AMP have different ones to be used with PHP, Python, etc.