In microservices environment deployed to the Kubernetes cluster, why will we use API gateway (for example Spring cloud gateway) if Kubernetes supplies the same service with Ingress?
Ingress controller makes one Kubernetes service that gets exposed as LoadBalancer.For simple understanding, you can consider ingress as Nginx server which just do the work of forwarding the traffic to services based on the ruleset.ingress don't have much functionality like API gateway. Some of ingress don't support authentication, rate limiting, application routing, security, merging response & request, and other add-ons/plugin options.
API gateway can also do the work of simple routing but it mostly gets used when you need higher flexibility, security and configuration options.While multiple teams or projects can share a set of Ingress controllers, or Ingress controllers can be specialized on a per‑environment basis, there are reasons you might choose to deploy a dedicated API gateway inside Kubernetes rather than leveraging the existing Ingress controller. Using both an Ingress controller and an API gateway inside Kubernetes can provide flexibility for organizations to achieve business requirements
For accessing database
If this database and cluster are somewhere in the cloud you could use internal Database IP. If not you should provide the IP of the machine where this Database is hosted.
You can also refer to this Kubernetes Access External Services article.