Wow! I tried, but with minimal .NET knowledge I ran into roadblocks everywhere due to lack of documentation. Do you know of any standard/idiomatic ways of defining viewmodels in F#? What about HTTP calls and JSON parsing?

HTTP and JSON are well catered for on .NET and Xamarin. Newtonsoft.Json is the most popular. And then HttpClient has first class support in Xamarin.

In terms of view models... how long is a piece of string? There are literally dozens of approaches one could take. Or you could use Xamarin.Forms which is a MVVM framework (amongst other things).