3. 저는/그는 -> uses 는 to reference a specific thing already mentioned or known in conversation/writing. 학생이 -> use 이 to describe some (general) thing and emphasize it. So 학생이 아니다/아니에요/아닙니다 -> It's NOT A STUDENT. The emphasis is on the fact that something IS NOT A X (here, student). It will always be important to emphasize what something is not. Therefore, this is a set pattern "N은/는 N이/가 아니다".

1. 아니다 vs 아니에요 There is absolutely no difference in meaning. The first one (아니다) is the plain/dictionary form. The second one (아니다) is the conjugated form in the 요 level of speech (present tense). The formal form is 아닙니다. 아니다 means "to not be". So, 아니다 used in the sentence and 아니에요 mean "am/is/are not". This is just like 이다 and 이에요/예요. Both mean "to be", but the first one is in plain/dictionary form and the second one is conjugated in 요 form (present tense). We know the formal form is 입니다. So in a sentence it means "am/is/are". 2. Actually, it would be more accurate to ask why it loses a particle at the end of it. (I would also like to point out it should be spelled 학생 in both sentences) To be exact, "N이/가 아니다" is the correct grammatical form. So in this case, "학생이 아니다/아니에요/아닙니다" would be all be correct. Let's look at the first sentence... This sentence is a lot more bookish, as evident by using 아니다 in plain form. Therefore, this sentence is more precise about following the rules and uses the particle 이. Let's look at the second sentence... This sentence is a lot more casual or conversational, as evident by using 아니다 in a conjugated (요) form. Oftentimes in speech, the particles 는/은, 이/가, and 을/를 are omitted. Since this sentence is more casual, it reflects a spoken style and omits 이, with no change in meaning. If you wanted to be technically correct, you could just as easily use "학생이" in the second sentence. But this sentence is meant to be more colloquial, so that's why it's originally omitted here. If context were clear, you could omit "저는" or "그는" too. So the second sentence is more like "저는 학생(이) 아니에요". It's just a matter of being colloquial.

'학상'is wrong word. only '학생' is right. if '학상' was used, it's dialect. Difference between '아니다'and '아니에요' is that '아니다' is literary style, and '아니에요'is colloquial style. literary style : -(이)다. ex) 아니다. 먹었다. 잤다. 좋다. .. colloquial style : -요, -입니다, and many other styles ex) 아닙니다. 아니에요. 아니야...