You can certainly connect multiple node-based app pods to the same database. It is sometimes said that microservices shouldn't share a database but this depends on what your apps are doing, the project history and the extent to which you want the parts to be worked on separately.

There are questions you have to answer about running databases at scale, such as your future load and whether you want to use relational databases if you're going to try to span availability zones. And there are some specific to kubernetes, especially around how you associate DB Pods to data. See https://stackoverflow.com/a/53980021/9705485. Another popular option is to use a managed DB service from a cloud provider. If you do run the DB in k8s then I'd suggest looking for a helm chart or looking at an operator, such as the kubeDB operator, to avoid crafting the kubernetes descriptors yourself and to get more guidance on running the DB and setting it up.

If it's a new project and you've not used k8s before then you'll also have to decide where to host your code, your docker images and your deployment descriptors and how to setup your CI pipelines. If you've not got answers to these questions already then I'd suggest looking at Jenkins-X as it will provide you with out of the box defaults for a whole cluster and CI setup and a template ('build pack') for building node apps and deploying them to staging and prod environments through a pipeline.