I would say あっちゃ, こっちゃ here in your example are the contracted pronunciations of あっちへ, こっちへ. うまい もも こっちゃ こい。<< うまい桃、こっちへ来い。 "Delicious peach, come this way." にがい もも あっちゃ いけ。<< 苦い桃、あっちへ行け。 "Bitter peach, go away."


As you said, this で is "at" (at a place). 日之出ん家で means "at Hinode's house". ~ばいいのに has the other meaning, which is a suggestion such as "why don't you ~". This する in the manga means "take a poop". So it means "Why don't you take a poop at (the bathroom of) Hinode's house?"


どうにもならない (not どうにかならない) and 仕方がない are similar like you say. どうにもならない is however reserved for significant things as it conveys irreversibility. E.g. the following is fine: 電気消すの忘れた 仕方がないな The following is odd because surely it's easy to go back and just switch it off. 電気消すの忘れた どうにもならないな The following is thus natural again: あー、家出る時電気消すの忘れた!もう飛行機あと5分で出るのに ...


Here 「こっちゃ」is a diminutive for「こっち」or「こちら」, simply meaning "here". 「あっちゃ」:「あっち」、「あちら」, "over there". Now they should make sense in the context.


名【な】 is "name", and Xという名の~ means "~ named X". This is a set expression. Xという名のならず者 a rogue named X 名の人 doesn't make sense. 名のある人 (or 名がある人) is another set phrase meaning "famous person".

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