TL;DR: First-person protagonists are never all-knowing, but if they're telling the story after the fact, they can know things they haven't been told yet.
First-person narratives come in two flavours: past-tense, where the narrator is recalling events that have already happened; and present-tense, where the narrator is describing events as they happen. Past tense is more common in novels, and present tense is more common in visual novels.
In a present-tense first-person narrative, the narrator cannot possibly be all-knowing. They learn things at the exact same time as the reader - or possibly even afterwards, depending on the reader's level of perception or genre-savviness.
In a past-tense first-person narrative, the narrator has the benefit of hindsight, and will know things they shouldn't know at that point in the narrative. To Kill a Mockingbird, for example, opens with Scout and Jem arguing over the exact chain of events that led to Jem breaking his arm, something that doesn't happen until the very end of the book. But the narrator's knowledge is still limited to their own experiences, and anything they may have been told after the fact, so they're still not omniscient like a third-person narrator can be.
To address the question you edited in while I was writing this:
If you're using a past-tense narrative, you can have the narrator explain what happened during their absences, under the pretence that they were told later. If you're using a present-tense narrative, and nobody ever fills the narrator in during that narrative, then they cannot possibly know what happened during their absence and you cannot have them describe it to the reader.