I've skimmed through the beginning of the second part of Euler's
Introductio in analysin infinitorum, where he introduces graphs. Somehow, he manages to do without the term "graph".
He calls them just
lineae, like
linea, sive recta sive curva, cujus natura a natura functionis pendet/ex functione resultat... Euler is careful not to omit
linea before
curva, but Gauss uses
curva on its own. This is in line with the modern usage of the term
curve.
As for the "plateau", my personal proposition not backed up by any authority would be just
aequum. It conveys the idea of something flat and is not tied to landscape. E. g. something like
summum aequum curvae pressionis respiratoriae.
Probably, both
algorithmus and
algorismus are fine. The term is derived from the name of Al-Khwarizmi.
Algorithmus has been attested for centuries, Gauss uses it and it entered modern languages, so personally, I'd opt for it rather than for the latter, more exotic spelling. (Curiously,
algarismo is "digit" in Portuguese.)
As for models in the mathematical sense, here we're on our own. I think it's a fairly recent usage. A mathematical mode is not something "exemplary". Probably, the original metaphor is that of a clay or wax model. But the difference is substantial. A clay model is used to produce a sculpture. Mathematical model is not used to produce anything. It's an imperfect representation of reality studied by mathematics. Mathematics itself doesn't go beyond models.
Since the model is a representation, perhaps we can call it
simulacrum? Cf. "a computer simulation".