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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.