Both are acceptable. It's just a regional dialect. You will hear the differences as you move very short distances in the UK. Often people in the same family say it differently with an i or an e. It is believed by British people that Americans prefer to say. With the i sound. There is even an old song about it. https://www.youtube.com/watch?v=zZ3fjQa5Hls

I've heard both in the UK, it's just how you have got used to pronounce it. I don't think it has something to do with social status or level of education. Probably just how it is/was pronounced in your family.

Both are correct pronunciations, although the British tend to stick with (I)-ther while Americans stick with (E)-ther. Say it how you want. :)

What about "assume" ?

Either. As in either way. Also look up "assume". That other way is so awful. :(