EA has falsefully banned my Apex account

Heya,

Account actions (Such as suspensions, bans, etc) cannot be assisted with on these forums, as this is a community space.
Only the TOS Team is able to assist with these matters, which you've already contacted.

You can dispute your ban up to around 3 times, anything after that will likely be disregarded.
So if they decided to uphold the account action, it's likely permanent and nothing can really be done to change the fact.

The ban reason should have been included with a mail sent to the email address linked to your EA Account.