What did the Romans call their language?
The answer to this question is a simple one; it was the Romans themselves who referred to their language as lingua Latīna—“the Latin language” (literally 'tongue').
Did Romans pronounce C as K?
In all of the mentioned Romance languages, the letter "C" is pronounced like a "K" would, as long as the "C" isn't followed by an "E" or "I".
How did the Romans pronounce g?
g before e, i, y, ae, oe is soft (as in gel): genitum (jeh-nee-toom); otherwise, g is hard (as in go): gaudeamus (gah-oo-deh-ah-moos). gn is pronounced ny: agnus (ah-nyoos).