After connecting to the ec2 instance, clone your code on it. It's not compulsory to keep /var/www/html but still it is considered a good practice. Clone the npm install directory in your project directory. It will install all the required packages to it.
Now for running you app in production you need a service like pm2, forever etc. use one of these services, configure it and then run your app on any port you want. for eg. if you're using pm2
$ PORT=4567 pm2 start app.js --name API --env production -f
Now you can use pm2 to check its status. your app should be running on https://server-ip:4567/ . You'll have to configure the likes of apache or nginx to forward requests recieved by your app to the port you selected. After that you'll be able to access your app without the port number. Chech this out if you need more help.
I'd say instead of doing this. move your application to a vcs like git. A lot easier to configure your application like that.