Anyone know the difference between "acabar" and "terminar", or if there are situations in which one is appropriate but the other is not?
Based on the apparent etymology (acabar < Latin 'caput' = "head"; terminar < Lat. 'terminus' = "end"), my gut instinct would be that "acabar" implies finishing by cutting something short, while "terminar" implies finishing by seeing something through to completion. (E.g., "acabo de leer" if I stop reading a book partway through; "termino de leer" if I stop reading because I finished the book.)
Is this remotely accurate?
I'd say that "stopping" something is to some extent independent of completing it - it is not expressly included in the meaning. It does suggest the possibility of interruption mid-completion, but in reality, one may have completed the task or not. Or, the "stopping" may be about something that has no inherent finite scope or duration, e.g. "He stopped going to the gym on Fridays" - no completion, simply the ceasing of an ongoing action or routine.
Meanwhile "finishing" indeed means completion of something that has a finite scope or duration.
The translation for "comiendo" is definitely "eating". But in different languages they may not use that tense as often as English does. So while we may say "eating", they would use the infinitive form (comer) or perhaps the present indicative (comes). For example, we may say "what are you doing" and while you could say "¿Qué estás haciendo?", the more common translation in my experience is "¿Qué haces?"
Hope this helps.