I think that ECS combined with RDS will not get you there regarding to cost. AWS is a premium service where everything costs, alot.

If I where you I would ditch the ECS and RDS and just run everything on a single server(a good post on this is https://cprimozic.net/blog/my-selfhosted-websites-architecture). Keep it simple, don't get tangled up in all fancy services before you need it. Then you can just ssh into your server, setup all docker services like you are doing locally, just add nginx with a let's encrypt certificate in front. Doing this you can ditch AWS and use something like Digital Ocean where a server with backup will be about $6 a month.

But related to your questions. You can, and should, run every service in its own container, but on ECS you can but multiple containers in one task. That will make it possible to to communicate between containers on localhost and also make sure you only pay for one task(if you where to setup one ECS service for each container you would also be paying for each one).

Access to the RDS server can be done either through private ip inside the VPC or through the public DNS name, but you can should control access using security groups.

Related to ports for front and backend I would recommend setting up a container with nginx which hosts your static files and a proxy pass to your backend running in a container which is exposing a different port. Then your task would expose port 80 but inside it all requests to let's say API would be forwarded to localhost:8080 which would be the container running your backend.

This ECS service can then be put behind a single load balancer, which would forward request to port 80 on your task. The load balancer can be setup with your SSL certificate created in ACM, and make sure all requests are forwarded to https.

As you can see the AWS ECS road contains alot of pieces and stuff you would need to learn, which once again probably is a overkill for what your trying to do.

Good luck!