Not gonna lie, my first attempt at this questions I said "My brother likes to eat nachos"
why ночью and not ночь? I have really hard time getting a hang of these cases...
Ночь is in the nominative case and means "night". Ночью is in the instrumental case and means "in/at night". Certain set expressions related to seasons and parts of the day do this when you're talking about being in this time period, for example: In the morning (утром), in summer (летом), in spring (весной), in the afternoon (днём). Notice that they don't use prepositions such as на/в and aren't in the prepositional case, they are all in the instrumental case. The instrumental case several different uses that aren't related to each other, this is one of them. There aren't many different seasons/times of day though, so you can memorize them individually instead of thinking about which case to use.
If i understand you correctly... let's compare two sentences: "Мой брат ест (что делает?) ночью." We have no "ь" after "т" in our question, that's why we write "ест" without "т". (My brother eats at night). Мой брат любит (что делать?) есть ночью.We have a "ь" after "т"? that's why we write "есть" with a "ь". (My brother likes to eat at night).
Could this be translated as "My brother likes to exist at night" Although it is improbable that this is the better translation of the two. Would this be how you say "My brother likes to exist at night" or would you use different words?