Hi there,
Yes, your customers can use the gift cards in your physical store, here’s how: https://help.giftup.com/article/21-how-to-validate-accept-redeem-gift-cards-in-person
With Gift Up! we ask you to attach your own payment gateway to us. This way you get paid in full, at the point of sale into your attached payment account. Gift Up! supports, Stripe and Square (both of whom we recommend for all of our clients), Mollie (who we recommend for our EU customers) and PayPal (who we actually do not usually recommend) to name a few, but not the WooCommerce Payment Gateway.
All of these providers are free to set up and do now have any monthly or set up fees and you can get up and running in a matter of minutes usually. They all also allow your customers to pay with a credit and debit card.
In terms of customizing the email, absolutely. You have lots of control: https://help.giftup.com/article/84-customizing-the-emails-we-send-to-your-customers