Balancing on docker swarm instances?

Question

Nginx

Colleagues, hello.
I am slowly "pollinated" by training docker clusters, how it all works, etc., etc.
Now in my clusterer there are 2 managers, 2 wokreers. A swarm has a dozen instances that look at the web.
Behind the cluster is a proxypass web server that proxies requests from the world to instances within the cluster. Now it works like this, but there are several questions:
1. how is it correct / better to implement such a scheme *?
2. there are some traefic and similar systems. or the usual good nginx for balancing is the easiest?
3. how best to "distribute" requests.
and now more about the scheme *
by-design now everything works for me like this:
user -> proxypass server that sends requests to the manager's ip:port -> manager -> backend (instance)
If you show on your fingers, then, let's assume:
proxypass ip 10.0.0.1
ip-manager1 10.0.0.2
ip-manager2 10.0.0.3
ip -worker1 10.0.0.4
ip-worker2 10.0.0.5
Regardless of where the instance is located (on worker1, 2 or manager), all requests from 10-0-0-1 go to 10.0.0.2, and then the "manager" will figure it out , where to send requests to, since instances in the local network are open on ports 10000-10100.
That is, for example, the nginx instance works in such a way that it is written in docker-compose:
ports:
- 10001:80
and, accordingly, in the proxy pass I will write 10.0.0.2:10001.
There are several questions at once, as I wrote above. First, how "correctly" am I doing this? Since, as I understand it, if manager1 stops standing for a while, then all requests will spill, since there will be nowhere to send them.
How to deal with cookies? Because if some wordpress works on three instances, then by round-robin I will hit three different instances three times, go through authorization three times ( in fact , because of this, the question arises, is it necessary to use LB in docker-stack cluster so that it stores cookies(?) ).
In fact, there are many questions, interest, to be honest, no less - something new and cool.
It will be cool if we can discuss and chat about this topic in the comments, thanks.