Having read your follow up information it may be worth talking to your son and explaining that we all have different strengths and weaknesses and he should not tease his sister about her grades but praise her efforts.
You should talk to your daughter about not teasing her brother as school as this is probably antagonizing his beahiour towards her when he gets home. They both sound like they are very different in personality and will treating differently when handling situations.
When you say about him having the biggest pick of dessert and always sitting in the front. Set in place a rota for who's turn it is to sit in the front and insist on equal portions of dessert.
It is right not to look for who's to blame when things happen. You are dealing with the situation very well allowing each child to have their say individually too. This behaviour is normal and just requires your consistency when dealing with the problems as they arise. This should help to keep things under control.
Their relationships will change and grow as they get older. In the meantime keep going, you are doing a fantastic job.
Please accept if I have answered your questions.