> In Japanese, an E column kana followed by I sometimes makes a long E, like in 先生 (sen + sei -> sensē).
While it is sometimes difficult to discern the combined E and I sound, especially for non-native speakers, the word 先生 (sensei) is technically pronounced "sensei" and should be spelled that way to distinguish it from words with long E sounds, such as ええ (ee) and お姉さん (oneesan). Similarly, the OU in 東京 (toukyou) and the OO in 大きな (ookina) are different and should be spelled differently. I hope this helps.
EDIT: Added a comma.
Sure, and in a Japanese song, "sensei" can yield four beats or notes SE/N/SE/I.
But spelling out and singing aren't normal speech. Spelling/singing can break apart diphthongs, like NAI becomes NA-I.
生 is not written with い due to the /e:/ having a different sound from that one in from おねえさん. It does not (when you aren't spelling). It is written the way it is for ancient historic reasons.
> Similarly, the OU in 東京 (toukyou) and the OO in 大きな (ookina) are different
No, they are't.
> I hope this helps.
こう言うバカな戯言は少しも誰にも役に立つはずないんだぜ。