It seems that for right now the best way to style components is this library:
This seems to be the best way so far. The only downside is there doesn't seem to be syntax highlighting for the css in these. Other than that this seems to be a rather complete solution to keeping styles in the components
Debugging is in very early stages but it does work. Start your app in debug mode in visual studio. Then paste the following into a terminal:
chrome --remote-debugging-port=9222 --user-data-dir="C:\\Users\\bbrougher\\AppData\\Local\\Temp\\blazor-chrome-debug" https://<<Your Debug Instance Here>>/
Then press Shfit+Alt+D to open up remote debugging for Blazor. A separate tab should open and you should be able to debug with the chrome debugger.
It looks like this page may provide some information:
Host and deploy ASP.NET Core Blazor WebAssembly
When publishing the server side, the wwwroot folder has anything that the client side needs. This folder can be deployed to nginx. The server side does not need to host the frontend.