Hi Jonathan
There is a maximum withdrawal limit of 500 euro per day per card. This cannot be raised.
Yes, it's possible to do payments through European (SEPA) Direct Debits. Please be aware many French companies don't comply with SEPA law and won't allow you to use a non-FR IBAN. But, they are obliged by law to accept them.
It's not possible to deposit cheques or pay by cheques. It's a dying payment method, also in France. The bunq team likes to look forward and facilitate modern and safe payment methods. Debit cards with branding of Maestro and Mastercard are widely accepted in France and should suffice as a standard.