Does the customer get an order confirmation email, and can I change it?

Yes. When an order is placed on your storefront, the customer is emailed "Your order #… is confirmed". It lists the items, totals and shipping address, and a PDF invoice is attached.

• Test orders don't send it.
• Orders you create in the admin don't send it either, unless you tick Email order confirmation to customer when creating the order.
• To get a copy of every email, add your address in Cc or Bcc on Settings → Web Settings → Email Provider. That page also shows how much of your monthly email allowance you have used.

You can't change the wording or design yet. The confirmation uses a fixed built-in layout, and the "New order" templates listed under Email Templates are not used for it.

If the email can't be sent, the order still goes through. Email Delivery Logs shows what was sent.