The penny or cent remains a unit of account despite being eliminated in Canada and approaching uselessness in other Western Nations such as the U.S. and U.K.
For financial transactions the basis point, a mere 1/100th of a cent, remains the most common unit in which prices and interest rates are denominated.
Basis points (BPS) refers to a common unit of ...
While in this case plenty of sesterces were actually coined, in general you might ask why the Carolingian Empire (and most of Europe for several more centuries) used librae in its accounts or why tribute to Athens was stated in talents, neither of which was ever coined. Uncoined units of account are a convenience that avoids the need of coins for monetary ...
I believe that honour belongs to Julia Drusilla, the sister of the emperor Gaius (commonly known as Caligula).
As explained in A Companion to Women in the Ancient World by Sharon L. James, and Sheila Dillon,
Members of the imperial family began to receive worship, especially in the Greek East, from the time of Augustus, but the first woman to be deified ...
Vivian Nutton provides a detailed account for the workings for a Greek/Roman temple like the Asclepeion in his book Ancient Medicine pp. 109-110.
At the shrine suppliants would purify themselves at a sacred spring,
before offering an appropriate sacrifice, and then, wearing white
robes, undergo a second purification before entering the abaton or an
Plutarch's Lives says this about Marcus Cato:
He would likewise say ... and that in his whole life he most repented of
three things; one was, that he had trusted a secret to a woman;
another, that he went by water when he might have gone by land; the
third, that he had remained one whole day without doing any business
Other than "Ave", "Vivat" ([long] live) comes to mind.
I have also found that in a toasting-cheering context, the proclamations "dii propitii!": (May the Gods be propitious!) and "Feliciter!" (be lucky, happy) were used.
The Wiki article makes quite a good job of demonstrating that "res publica" was used to refer to many different concepts: