I noticed my Docker-containers doesn't get local ip-addresses.
That's normal for bridged and overlay networks.
My Plex installation gets a 172.17.x.x address and my MariaDb/phpMyAdmin aswell. Is there a way of fixing this?
You can. You need to create a docker macvlan network for this. Its slightly complicated and I am not going to share the commands required to do it. I am a container pro (I make my living with it) and I don't like it and I don't use it. There are not many use cases that realy require a macvlan. I am sure others will chip in and share what's needed to get things up and running.
When watching Plex at home on my network it always transcodes because it thinks I'm not on the same network and it's a bit disturbing.
You can either run your Plex container in the host network or set the "LAN networks" in PMS's settings -> network. My value is "192.168.200.0/255.255.255.0,172.16.0.0/255.240.0.0". My local LAN is 192.168.200.0, replace this one with yours.
EDIT: I've checked the "network" tab in the Docker-UI and the "bridge"-alternative and I can see the IP-range there but I can't change it?
Thanks.
You can't, it's immutable. Even if you could, containers on such a bridge would behave like they are on a switch that is not connected with the rest of your network.
Instead of tryting to enforce old patterns to docker, I highly recommend to learn and understand docker, and then start doing things the docker way...