.NET:
As long as you run BC on an "OnPrem" environment (target = OnPrem in the app.json) you can use .Net in the same way NAV allowed you to so.
In case your company will go for the Saas version, you will have to find workarounds. Like putting your .NET-functions into AzureFunctions and consuming those, or creating a Service in your OnPrem environment and access your old functions by calling them with webservices.
WebDevelopment:
yes, you can use Control-Addins to use javascript and generate any HTML-Output you like with that. (inside an Iframe in the BC Web App)
Here is an introduction:
docs.microsoft.com/.../devenv-control-addin-object
VSCode in general supports all kinds of languages, so you can program all of this in the same environment.
