1) I use my site, plus while at home, I use Grafana. It's a bit better at looking at some random time period. I kind of did it to get familiar with MQTT, Influx and Grafana, but I've gotten to like it.
2) I use a custom skin based on the original - I started more than 5 years ago. I added steelseries gauges, an earthquake map, swimming pool temperature, air quality and other stuff over time. There are so many popular skins, I'd look at the
https://weewx.com/showcase.html page for inspiration
3) I hate the idea of needing an app to view a web page - I just view the web page on mobile. It works fine.
5) extensions - figure out what you want to do, what you want to show, and add the extensions as you need them..