Hello!! Some people in Korea have told me that they sound different, but some people have also told me that they sound the same. To me, they sound the same, but you are right about how the vowels were formed. (I've been told that in the past, they were made to be different.) Besides sound, in writing, you have to be really careful with when to use them. For most nouns, you do have to memorize which words use which, but after studying for some time, you may notice some patterns to help you remember. Also, there are some word forms that are related, and you will notice that there can be a relation between 아 and 애. For example, You may learn, if you want to say: He said he's a student. -> 학생이라고 했어 or 학생이래. Here, you see a relation between 라고 and 래. It might help to study Chinese characters as they are used in Korean, as well. Many Korean words come from a combination of Chinese characters, and then it may be easy to memorize which are ㅐ and which areㅔ by remembering the meaning of the character. For example, one meaning of 재 is connected with "repeat" or "again," i.e. 재활용 하다 in "recycle." one meaning of 제 is "manufacture," i.e. 제품 in "product" or "manufactured good." I hope that helps!!

"ㅔ" and "ㅐ" are a single vowel. First, you should pronounce "ㅣ", and then lower down your lower jaw so as to pronounce "ㅔ", and then lower your lower jaw more down, then pronounce "ㅐ". "ㅣ<ㅔ<ㅐ"

No specific rule. You just have to memorize that which is used in which word! Not a clear distinction between them!