Yes by default, IF the project is not deleted from your account (you still have to pay for quota if you hit the form submission limit based on the hosting plan). This Zapier trigger is just a webhook when the form submission handler on Webflow’s servers receive the email, which will still be IF the default form action is unchanged.
No, IF you specify/change the default form action. That means you have implemented a third-party email handler (pointed the emails to be sent elsewhere). Whether you can use Zapier or not depends on the service.