I'd like to create a custom field in Marketo which is not synchronized with our CRM.
I have created the field (type: string) in the admin and I don't find where I have to enter the values which will be stored (for a picklist).
I know how to enter the values for a form but not for the database.
A custom field created in Marketo will not be synced to CRM (unless you ask Support to manually map/sync the field to a field in CRM). That only works when you create the field in CRM - and then select it as a synced field in Marketo. So you're good there. The values for a picklist are done at the form level. You cannot define the values at the database level.