1) You can set your paypal account to send email notifications when an order is placed. see this link for details:
You receive money
Special notifications or surveys are sent to customers
You receive a Website Payment or Auction Logo payment
Here's how you can view and edit your notification emails in your account profile:
Log in to your PayPal account.
Click My settings.
Click Update beside "Notifications."
Check or uncheck the boxes under Payment Notifications according to your preferences.
You can also change your settings to stop receiving payment notifications by following these instructions.
2) yes, Paypal will send the customer a receipt.
with paypal standard, you would need to configure an IPN Page. when paypal completes the transaction, it will make an IPN Post to a page you set up. on the ipn page, you can trigger sending the email.
there are many threads throughout this form dealing with the limitations of paypal standard, and IPN.