I have read plenty of literature in this context (see links below). The presence of classic vs new Azure management portal, Roles vs App Services, Azure Website vs Azure Web
RE:Can I RDP to Azure App Service Web App underlying compute resource?
No, you are not allow to RDP into the machine. You application is running within a sandbox, depending on your plan, one machine might running multiple sandbox from different user.
RE: Can I install custom third party software components (e.g. Crystal Reports) to Azure App Service Web App underlying compute resource?
No, the machine will upgrade periodically, content might be reset. Also user that app is running on will not have the privileged to install application. If your application is depending on other dependencies, e.g asp.net web application, you should specify all dependencies during build time (nuget).
Check the first two reference you provide, they are talking about Azure Virtual Machine, not Azure App Service, where Azure Virtual Machine is SaaS, Azure App Service is a PaaS. If you are looking for something in the middle, please try Azure Cloud Service, it supports RDP and I believe you should be able to install third party apps with on start script.