Maybe because my first language is Spanish and not English (or maybe because I'm "corrupted" after studying Ancient Greek and I remembered ἵνα), I translated it as stop to eat (literally) but I understood it as stop for eating. But να is the construction for the infinitive, yes. How would it be stop for eating?
Να, yes, it comes from the Ancient ἵνα. After να Modern Greek use subjunctive. Να τρως is present subjunctive , να φας is aorist (past) subjunctive. For the verb τρώω or τρώγω, that is irregular in tenses, take a look at http://www.lexigram.gr/lex/newg/%CF%84%CF%81%CF%8E%CF%89#Hist5 for all the tenses available.