Yes. You need to configure plugins like WooCommerce Stripe plugin or PayPal Standard etc, to support recurring payment in your site.
Yes. It supports Paypal and Stripe payment gateway plugins.
Yes. You can use the synchronization feature for a specific purpose.
Yes. The customer/subscribers will receive emails regarding their subscription activities like renewal, activation, renewal, payment failure, etc.
Yes. Using the change payment method option available under the user my-account page, a user can always change their credit card for an active subscription.