Does the Anglican Use have the capacity and resources to celebrate daily mass and if so, are there any Ordinariate communities which do? In the Roman rite we have the Tridentine liturgy (Extraordinary form) and the Novus Ordo liturgy (Ordinary form). Both of these liturgies have unique liturgical calendars, and unique cycles of scripture readings and liturgical prayers (aka "Propers") that cover every day of the year. The Tridentine Liturgy completes a cycle every year, while the Novus Ordo takes 3 years to complete a single cycle.

The important point is that it is possible for a priest to say mass on any day of the week on any day of the year using either of these liturgies and there will be associated prayers and readings specially selected for that particular day.

My question is, does the Anglican Ordinariate also have it's own exhaustive liturgical calendar, with set readings and prayers for every day of the year? Such that an Anglican Ordinariate Community could celebrate mass in the Anglican Use on any day of the week on any day of the year and still have their own unique set of readings and prayers for that particular day of the week?

And a follow up question, if the Anglican Use does have it's own cycle of prayers and readings, are there any Anglican Ordinariate communities who do indeed celebrate mass every day of the week, every day of the year according to this cycle of readings?
My question is, does the Anglican Ordinariate also have it's own
  exhaustive liturgical calendar, with set readings and prayers for
  every day of the year?


Yes.

Information about the ordinariate's missal is here. 


  Such that an Anglican Ordinariate Community could celebrate mass in
  the Anglican Use on any day of the week on any day of the year and
  still have their own unique set of readings and prayers for that
  particular day of the week?


It's worth noting that this is a relatively recent innovation. The Extraordinary Form (Traditional Latin Mass) of the Roman Rite does not have a daily lectionary with different readings for each day of the week.


  are there any Anglican Ordinariate communities who do indeed celebrate
  mass every day of the week, every day of the year according to this
  cycle of readings?


Yes, some have daily liturgy. You can see a list of parishes and their liturgy times here.