Are there equivalents of _Sent data views for Mobile Connect/Push that will allow me to get information about SMS/pushes sent to particular subscriber? I know this information is visible in All Contacts but is there a way to populate a data extension with it? Maybe there is something Salesforce can do to make it available as data extensions.
You can have sent data in Push Send Logging: https://help.salesforce.com/articleView?id=mc_mp_send_logging.htm&type=5
You can also have data on device and tag level: Attributes in _PushAddress and _PushTag Data Views