The Ur-Sphinx - Intelligence

The Ur-Sphinx rewards casting expensive Sphinxes ahead of curve and attacking with as many of them as possible. Every attack mills the whole table and hands out a free spell to everyone, including you and your opponents.

"As long as The Ur-Sphinx is in the command zone or on the battlefield, other Sphinx spells you cast cost {1} less to cast" is an Eminence ability -- it applies while this card is in the command zone, not only once it has been cast. The discount only reduces generic mana in another Sphinx spell's cost, and stacks with other cost reducers such as Unesh or Urza's Incubator.

Unlike Eminence, the mill/free-cast ability is a normal triggered ability of the permanent, not an Eminence-scoped effect. "Whenever one or more Sphinxes you control attack" can only trigger while The Ur-Sphinx is on the battlefield to see the attack happen -- it does not trigger from the command zone.

The ability triggers once per combat when one or more Sphinxes you control attack -- it is not a separate trigger per attacking Sphinx. "That many" sets the number of cards each player mills equal to the total count of attacking Sphinxes you control that combat.

Every player mills, including The Ur-Sphinx's controller. You may cast a card from your own mill under the same free-cast permission as any other player's mill.

A land card revealed by the mill cannot be cast under this or any ability -- lands are never cast, they are played. Only nonland cards milled this way are eligible for the free-cast permission.

Casting a card "without paying its mana cost" is still casting a spell -- all normal timing restrictions, legal-target requirements, and mandatory additional costs (including alternative costs that add extra costs) must still be paid or satisfied. If the mana cost includes {X}, X is 0 unless another effect allows choosing a value.

Once the mill/free-cast trigger has been put on the stack, it resolves independently of what happens to The Ur-Sphinx afterward -- the ability does not need its source to still be on the battlefield to resolve, only to have triggered in the first place.

Chain Eminence with Unesh and Urza's Incubator to push a curve of six-to-nine-mana Sphinxes down into the early-to-mid game, then attack with as many as possible each combat.

Use Roaming Throne to double the attack trigger and Windreader Sphinx to reward the same wide flying attack with card draw, converting one attack step into multiple mill/free-cast and draw events.