I think sid is like this because he has a neglected and lonely childhood as he said in the episode ki "itne bade ghar mei akela hi paya hai Maine khud ko, papaji mil jate the kabhi kabhi". His father has given him money, lifestyle but no time and no guidance and a child needs parents guidance and now when he has turned out like this so irresponsible and carefree, he suddenly wants to send him to dairy farm... Seriously?
But I think being raeeszyada and lonely still he has turned out good at heart. He is not arrogant, respects his Mohan bhaiya, has warm relation with Mrs Batra, even being thirsty offers his water to Bala, tries to make him sleep in whatever way he feels he is helping, He has the guts to accept he has lied to sanjana, he obviously cares for her feelings.
He is not leaving because he has hope that sanjana will say yes, sanjana never told him that she doesn't love her, she told him that "is janam mei to pyaar mumkin nahi hai kyunki hamari dono ki duniya bagut alag hai". So now sid is trying to match their lives to get her, any person in true love will do that.
Yes lying was wrong but that was in that situation because he wanted to enter academy desperately and saying that he is dying was very very wrong but atleast he accepted and he is ready to pay the consequences..