You currently have two options for hosting backend part viz nodejs server and mysql database for free:
1)Openshift:
OpenShift is an open source PaaS by Red Hat based on top of Docker containers and the Kubernetes container cluster manager for enterprise app development
2)Heroku:
Heroku is a platform as a service (PaaS) that enables developers to build, run, and operate applications entirely in the cloud.
They both provide containers for selecting technical stacks and are quite useful for development purposes.
For the frontend part github pages might be a good option and also other free webhosts can give you sufficient space to store smaller projects.