I need insights/suggestions for going in right direction and I guess it won\'t be an easy task. The requirements are:
First concentrate on creating well working msi installer for ASP.NET application only - point 4 - and perhaps just use self hosting app. This would significantly simplify deployment as one of he prerequisites (.NET Core) does not have to be bootstrapped - you remove point 1 of todo list. I understand that at this point you should be capable to install you ASP.NET app into IIS.
Tutorials and articles which may be useful for this part are:
Creating a WiX installer for ASP.NET Web Applications
Packaging a self-contained .NET Core app for Windows Installer
How To Create Windows Installer MSI - .Net Core Wix - video
The next steps would be to learn how to install prerequisites but I am sure once you will get your ASP.NET installer working all other items from todo list will not require further external advice.
You should be aware that both WiX toolset and msi installation technology have steep but not very long learning curve.