"I use eggs for today's meal."
Well, ni describes that something is a part of, or within something. If you do not use "ni", you are essentially saying "Today's meal is using eggs", and that focuses the word "using", instead of containing. It's kind of impossible to translate what it means, but it implies that the meal itself is using the eggs.
Just imagine a chocolate fountain that's nothing but egg yolk.
The topic particle just sets the focus on something specific, so the meaning doesn't change much. For instance 今日は料理にたまごをつかいます answers the question of "what I'm doing today". 今日の料理に卵は使います answers the question of "whether or not I'm using eggs". But the resulting action is the same.
Well yes and no, the thing is duolingo wants translations instead of interpretations, and adding "will" would make it a future tense which really doesn't exist in Japanese.
You're not wrong, and it would sound more natural in english, but since we're translating you need to watch out for things like this
私は in almost all cases is a given and a pointless addition, the focus is actually something being used in a meal, that's why you need には, it's really hard to ascertain where the focus is in an english sentence, but it's usually near the middle in longer sentences and near the start in shorter phrases.