Support

I removed the download key and secret word in the options. Not sure it was necessary to remove the secret word.

No, these are two different things. The Download Key is part of your account here at Akeeba. It's used to download updates. This should be removed.

The secret key is used for taking backups remotely. This is a pro feature which will be removed when you downgrade them to the Core version. No need to remove it.

Can she still use Akeeba ?

Yes, mostly. There are some features which require an active subscription such us uploading to Dropbox which immediately stop working after removing the Download ID. But this is a moot point since you're interested downgrading the to the Core version/

I would like to downgrade to the free Akeeba backup version for her, what's the procedure for that ?

Install the Core version on top of the Professional one. Everything else is automated.

By doing that your (ex-)client will no longer get access to any of the professional features of Akeeba Backup including remote backups, transferring backup archives to remote storage services and integrated restoration. Locally stored backups are not affected. Retrieving backups stored in remote storage is affected; they will not be downloadable until they either buy the Professional version or pay you (or someone else) to maintain the Professional version on their site.