Xamarin isn't based on the .NET Framework. It is based on Mono which is in turn already consuming a lot of code from CoreFX (== .NET Core) and that share will only increase over time.
Source: I'm working on the Mono BCL+Tools team at Xamarin/Microsoft.
It's true that .NET Standard 1.0-1.6 had a lot of gaps but these should be rectified with 2.0 now so you shouldn't run into these problems anymore (otherwise there's usually a good reason why a method/API is missing from the standard).
Disclaimer: I'm working on Mono for Microsoft/Xamarin, primarily class libraries and tools.
I'm a bit surprised that you don't seem to have an equivalent of the Handysignatur [0] (eID based on mobile phone) we have in Austria. It's getting more and more popular here, I guess because all you need is a mobile phone (who has a card reader after all?).
I find it incredibly convenient as it gives you immediate access to a growing list of e-government services [1], as well as signing PDFs and even things like a service for cancelling subscriptions online [2].
No, it should run on the 4.5 profile just fine as backwards compatibility in the .NET APIs is very good.
Please note that this is still a draft and the .NET 2.0/3.5 assemblies will likely reappear as reference assemblies (i.e. containing only method signatures in IL, so you can build against those profiles but not run on them).