Translation:Ik beloof om goed te eten.
Does it really matter whether I use "om" or not, in sentences like these?
Not really, although in spoken language, native speakers are more likely to include "om" than to leave it out. I think its presence makes it easier to parse the sentence.
why should we use "eten" but not "eet" here? It is not plural
It's the infinitive ('to eat' = 'eten'). The verb that's conjugated is 'beloven', which is in this sentence 'beloof'.
Quite clear. Thanks!