Wallets
It is possible to interact with the official wallets using two different techniques:
With so called deep links it is possible to open applications and navigate inside them. Deep links are URIs, whose custom protocols can be registered in the operation system, telling it what application should be started. This works also for mobile applications. Deep linking is usually an uni-directional communication, i.e. the wallets do not return nothing to the caller. (Although, this would be technically possible if a callback url would be considerered)
Signum has a specifcation how deep links needs be built, but it's usage depends on each application itself. At the moment of writing the Phoenix Desktop and Mobile Wallet supports a simple payment command, but at least a generic signing method is planned.
Deep links do not work with standalone versions of the desktop application as the protocol handler won't be configured.
The XT wallet uses a bi-directional communication protocol, which allows web applications to communicate with the extension and listen to account, network or permission changes inside the extension.