でた, いてる, でない: Are they incorporating (or equivalent to) ～いる or not?

Question

Each of the following sentences seem to be nearly unrelated, however I'm not sure if these sentences are incorporating ～いる in someway or not. I have looked at quite a few resources for each individual sentence but can't come to a conclusive understanding for them. Each of them are from the subtitles of the anime Non Non Biyori.

1. In Episode 1 ~5:28

Context: Almost none, Renge is talking to Natsumi and says:

朝飯につくしのお味噌汁でたん
Translation Attempt: I had horsetail shoot miso soup for breakfast.

While I'm pretty sure my translation is somehow correct I don't understand the でた at the end there. Is it just the past tense/contracted form of 名詞～でいる, in which it means something like, "it was."?

2. In Episode 4 ~6:35

Context: Renge's oldest sister, Kazuho, is talking to Renge about their other sister Hikage who should be on the way back home. Renge is confused and thinks Kazuho is talking about herself coming back despite her already being there. Kazuho says to clarify:

東京の高校いてるひかげ姉ちゃんね
Translation Attempt: It's your sister Hikage that (is in) (is going to) a Tokyo High School.

With いてる here I don't know if this is the progressive form of いる or the perfect form of 行く. To me, 行く makes more sense but I feel like that isn't correct because whoever wrote the subtitles left the word in all kana and it has no っ between the い and てる. On the other hand if it's いる changed into いてる, then what is even the point of that since いる is already stative?

3. In Episode 4 ~8:55

Context: Hikage is back and is talking to the new girl Hotaru (and some other girls). Hikage having just come back from Tokyo, is acting pompous. Hotaru was born and raised in Tokyo, but when Hikage asks her if she has ever been on the 新幹線, she says she has never been on it. Hikage then says:

おやおや新幹線をお乗りでない

I'll leave out a translation attempt here.
With my understanding, でない＝ではない without は and still roughly means "is not", however, this translation doesn't seem to fit. Although not probable, especially with the お honorific and the general impracticality, is this 乗る(stem form) + でいる (negative)? Is it actually 乗り (the noun) + でない (neg. of である)? If the latter is true, then how is it taking を and how is でない to be translated into English? All in all, I'm quite lost on this one and I'm probably overthinking it.

With these, in order to gain a better understanding, I could really use some assistance on the translations. Any help is certainly appreciated.

Answer 1

They are speaking some dialect. From the second one I thought it was Kansai-ben, but if the first was not a question but a statement, it is unlikely. It must be another dialect, if not fake Kansai-ben.

1. Either way, this is 出たん. In standard Japanese it would be something like 出たの or 出たんだ. Here it means miso soup was served for breakfast. A Kansai-ben speaker would say 出てん.

2. いてる simply means いる in Kansai-ben (Osaka-ben). I never use this form though I’m a Kansai-ben native.

3. This is standard Japanese. As you guessed, でない is a negative form of だ. She could have said お乗りではない, as well. It is an honorific form of 乗らない, or 乗っていない in this context. Actually, を is a bit weird. に would be more common.