Translation:At the dinner yesterday, I did not pay.
Well the meaning is basically the same, the answer is still wrong and here's why:
The first part of the sentence 昨日の夕飯 (Kinou no yūhan - Yesterday's dinner) で (de - At) は (wa - topic marker) clearly marks the topic which is "At the dinner yesterday". The second part お金を払いませんでした。(okane o haraimasendeshita.) means "I didn't pay".
I feel like 昨日は夕飯を払いませんでした (Kinou wa yūhan o haraimasendeshita) could be the Japanese version of your answer but it would be nice to have it confirmed with someone who speaks Japanese.
Yes, the 夕 kanji means "evening" by itself, and it's also a part of other common evening-related words, like the "dinner" or "evening meal" (夕飯 - ゆうはん) in this sentence.
You can find more examples here: https://jisho.org/search/%E5%A4%95%20%E3%82%86%E3%81%86
Regarding the similarity, I think it's a good idea to keep in mind that katakana words generally have multiple characters, so if you see a single katakana-like character followed by hiragana or kanji, then it is probably a kanji.
There are other kanji-katakana lookalikes too. For example 工 (こう) means craft or construction and it looks like エ ("e"), 力 (ちから) means power or strength and it looks like カ ("ka"), and (possibly the most obvious) 二 (に) means two that looks like ニ ("ni").
If you're interested, you can find other similarities here: https://en.wiktionary.org/wiki/Appendix:Easily_confused_Japanese_kana#Kana_with_Kanji
I'm not trying to nitpick here, but isn't "I didn't pay at yesterday's dinner" or at least "I didn't pay during yesterday's dinner" acceptable as well?
I get that this sentence probably refers to paying FOR the dinner and that sounds more natural, but without context, I think it's still quite ambiguous (especially to someone who's not a native English speaker as myself).
By the way, the two correct translations that I've come across for this sentence until now are: "I did not pay for yesterday's dinner" and "At the dinner yesterday, I did not pay". This also suggests to me, that my versions could be okay. Don't hesitate to correct me if I'm wrong though. Any input is appreciated. :)