Hey, I'm no expert, but may be able to point you in a helpful direction. A lot of this is really up for you to decide, as you can architect web applications like this in many ways. To jump directly into each question individually:
Frontend = ?
Login & Auth server= ? (Auth I guess Jws auth server?)
I would think this really depends on your backend. For example, you can use Node with Express and create auth middleware that will execute to authorize requests before doing anything else on your application, but you could also direct login routes to a separate auth server running on the backend and have your applications backend receive the "successful auth" message from that external service. This is definitely the aspect I'm least versed in, so sorry for the lack of a better answer.
Container = ?
Like you said, Docker can probably do the job here. I'm no docker expert but I don't see why you couldn't containerize both your front and back end so long as you configure the containers and the networking such that they can communicate.
Backend = ?
Frontend & Backend Communicator = ?
I have personally found great success in using the backend to create a RESTful API, and interacting with that API from the front end to "communicate". I find this very clean and convenient, and has the added benefit that if it ever becomes a future requirement, accessing your backend API from other applications is simple so long as it is written RESTfully and the networking for it's container is configured (since you said you want containers).
MySQL database for login = ?
MySQL is a specific SQL database, so I'm going to assume that you mean which SQL database to use. I've been enjoying postgres recently, and I know DO uses postgres for DBaaS. Otherwise MySQL would do fine - though I'd avoid Oracle SQL because I have had bad experiences there in the past.
See Edit: If you don't care about the database being SQL, you could always go for something non-relational like Mongo, but if you're already familiar with SQL this would just be another new thing to learn. Up to you on that one really.
Edit: I have been informed that Mongo has not been recommended recently and people have many gripes with it. Given that, I'd look into other NoSQL options if you want to go down that route - I'm mostly a SQL guy myself.
Again I'm no expert, but these are my 2 cents. Figured I'd leave a comment since no one else has yet.