(1) Yes, SSL is supported on Android.
However please note, that server certificates are validated using the System functionality. There is no public API for adding server Certificates into Certificate Store (this is supported on desktop only).
There is no support for client certificate authentication. If you need this, please let us know.
(2) No, there is no UI for Android or Win 10 mobile. You can either use UI-less
VirtualTerminal or implement your own screen renderer.