Why do I get a 10002:Security error Security header is not valid when Paypal Pro is activated?

You need a different API credentials for sandbox. The live API credentials is a only for production.

You can create a sandbox account and generate API credentials from the steps below:
Go to https://developer.paypal.com and login
Click on Test Accounts link
Click on 'Preconfigured' next to Create Account
Select United States for the country
Select Seller for the Account type
Enter a login email and a very simple password
Select Visa for the card type and select Yes to add a bank account
Enter 100 for the Account balance
Click on Create Account

** If you get an error message about the account creation failed, logout, clear your browser cache and cookies and try again ****

Once the account is created, select it and click on Enter Sandbox Test Site
Click on Merchant services
Click on Website Payments Pro
Click on Submit / Accept billing agreement
Follow the steps on the page to complete the billing agreement
To generate the API credentials
Login to the sandbox account
Click on Profile
Click on API Access
Click on Request API credentials / View API Certificate
Follow the steps to generate an API signature or API certificate.
* If you have an API signature and you want an API certificate, remove the credentials and request the right one. Note, removing the credentials will disable that credentials if in use.

Also make sure you are using the right API endpoint
Environment Authentication Calling Endpoint
Live API Certificate Name-Value Pair https://api.paypal.com/nvp
Live API Signature Name-Value Pair https://api-3t.paypal.com/nvp
Live API Certificate SOAP https://api.paypal.com/2.0/
Live API Signature SOAP https://api-3t.paypal.com/2.0/
Sandbox API Certificate Name-Value Pair https://api.sandbox.paypal.com/nvp
Sandbox API Signature Name-Value Pair https://api-3t.sandbox.paypal.com/nvp
Sandbox API Certificate SOAP https://api.sandbox.paypal.com/2.0/
Sandbox API Signature SOAP https://api-3t.sandbox.paypal.com/2.0/