Hi @alessandra11d,
Just to double check you do have the appropriate emails for your customers enabled? This means there would be a purple check mark next to the Email name column.

Link to image: https://cld.wthms.co/HfAoDu
Most commonly an order comes into your site as pending, but it may depend on the payment gateways you have available and their setup. Double check that those are set and enabled correctly first.
From there also try installing a plugin like Email Log that will create a log every time an email is triggered. With that activated place a test order and check the log to see if the emails show up there as sent.
Let us know what you find!