Are Free Apex Coins legal and do they work?

Just to add on to what everyone's mentioned here, I would HIGHLY recommend going through this page if you've ever entered any of your account information into another site.

https://help.ea.com/en-us/help/account/how-to-maintain-account-security/ 

It's extremely likely that those types of websites are phishing sites intended purely to collect account information and attempt to compromise your account.

Those scammers will also often take that information and see if it can be used to access any other types of accounts (emails, bank accounts, etc.), which is another good reason not to use the same login information for multiple accounts.

Keep yourself and your information safe!