So, Japanese does not diphthongise its vowels. By that, I would expect “Kansai” to be said “kan - sa - i”. Instead, I hear people saying “kan - sigh(English word)”. Which is right?
What is the pronunciation of “ooini” (very)? Is it “o - o - i - ni” or “ou - i - ni”?
I thought “ei” meant long E. For “sensei”, is it “sen - se(long E)” or “sen - say(English word)”?
This has been discussed pretty extensively, and presumably searches for things like “long vowel” and the various hiragana combos you mentioned should pull up plenty of reading material. There might be some specific topics that deal with your thoughts exactly, so maybe if someone comes across one they can link to that.
For sensei, the long E that you describe is probably more down to how the pitch accent is attached to the word. Nailing a correct japanese pronunciation is pretty difficult but there are some good resources around that can explain basic rules