yes, as you may have read in my earlier post, there is no rsyslog in the ubuntu container so I had to install it; then weewx started running

regarding the webpage (you mean the [e.g. Seasons] skin I guess)
a) you need to have a webserver installed (apache2, nginx, ...)
b) you need to put the HTML_root in weewx.conf to /var/www/html/weewx, where the subdirectory weewx might first need to be created:
mkdir /var/www/html/weewx
and in weewx.conf
[StdReport]
HTML_ROOT = /var/www/html/weewx
then you should be able to see the updated skin pages via IP-address:your-selected-port/weewx
e.g. 192.168.1.99:8000/weewx
but, you need to have changed the listening port for your container webserver from 80 to 8000 (and restart the webserver)
in apache2 this done in 000-default.conf (/etc/apache2/sites-enabled/000-default.conf) first line
and in /etc/apache2/ports.conf - replace entry Listen 80 by Listen 8000
you cannot use port 80 in the container as it holds the same IP address and 80 conflicts with the webserver of your NAS - therefore you have to run/let listen the container webserver at another port - I chose 8000 - that's what I used in the examples