I typed "He stopped eating," and Duolingo says this is incorrect. Is that actually the case? In English there would be an extremely subtle difference between "he stopped eating" vs. "he finished eating", as "he stopped eating" kind of implies that his meal was interrupted. It's not clear to me if this would be the same in Portuguese, or if Duolingo is just being difficult in what translation it takes.
Sometimes you don't need to worry about things like this, for example "he started to eat" and "he starts eating" mean the same thing. To me "he finished eating" is the clear choice because "he finished to eat" sounds wrong. I think it is just a case of knowing which words can be followed by the gerund (-ing form) and which can be followed with the infinitive (to form). Sorry, this is probably not very helpful.
Here are two more examples to illustrate the fact that there can't be a simple rule in English. Consider "he stopped to eat" and "he stopped eating". Both forms work but mean different things. Now try "he wanted to climb" and "he wanted climbing". Here it is the form using the gerund which sounds odd.
So far in my replies we have seen: both forms work and mean the same thing, both forms work and mean different things, only the gerund form works and only the infinitive form works. I hope all this is not too confusing.