I think, nowadays, Koreans use '반말' when they meet a person who they thought him/she is pretty close to them. (But, you should think again in formal place... it quite difficult.) So, many Koreans use '반말' to their parents, and other very 'close' elders. It's a kind of a family policy. This case, selecting proper word is more important. Maybe the "오빠" wants to put words(말을 놓다) with you. Most Koreans don't use '반말' with no cause(even just one mention, they need a trigger for change. Especially both have different ages.). And some Korean guys fear that youngers use '높임말' to him, they thought people consider him as a stiff man(I think it's serious stuff :D). Except second case, anyway, using '반말' is maybe good. If you confused, asking him/her will be a best choice. And, '저' is not using with 반말. '~요' is informal 높임말. So, it can match both 저 and 나(but, '저' would be good). On the other hand, formal 높임말 '~니다' , it must be match only '저'. * Also, there are more 반말. 1 informal and 2 formal. But, formal 반말s are very rarely used.

The first rule is if you have a very close friendly relation with someone, you can use "반말" no matter how they are older than you. The second rule is if you just met someone and they are strangers, you should use "높임말" even though they are of the same age as you. The first rule could be applied to your first and fourth question and t he second rule to the second question. As to the third questions, we usually do not use "높임말" to classmates unless a new school term just started and they are strangers.

Haha .. Not easy... But it is sure if you meet someone at the first time, you should use 높임말 eventhough your classmate or very same to your age except very young boy/girl. So I can say there is no relation between 반말/높임말 and someone's age. For example, my youngest sister who 7 years younger than me tell me '오빠, 가방좀 집어줘' but my brother, 3 years younger than me, use 높임말 to me. I use 반말 to my aunt ,she is 20 years older than me. But to my nearly friend, just only 1years older than me, I use 높임말... haha.. Sorry that i am sure the conclusion is that there is no perfect answer....