Nobody is happy because nobody wants to be happy.
Adhya needs Anuj and Shru to be together to be happy. Her father is not letting that happen wholeheartedly so she is unhappy. She wants to fix other people's lives to be happy. It does not work like that, unfortunately.
Anuj wants Anupamaa but Anu comes with some unavoidable situations and many misplaced priorities. So he can't be happy.
For both of them to be happy together it's important that either she sorts out her life or he accepts that things can't change. So either he compromises with everything or he moves on. He can't do both so he can't be happy. He should join some meditation classes and now shift his focus from worshipping Anupamaa to worshipping God and work on his liberation from his world which is full of suffering. Buddha says desire is the cause of all suffering. He should try to rise above his worldly desire to get Anupamaa. 
Anupamaa can never be happy. It's her fate that happiness will come in bits to her. She wants to be a Goddess while being born as a human. For her to be happy she wants to be everywhere, do everything, fix everything, be venerated by everyone, and made to be sit on a pedestal. Until then she can't be happy. Criticism, complaints, and challenging situations are unacceptable to her.. Usko sab sab sab chaiye and its a universal law ki sabko sab nahi milta. Most importantly she needs to be worshipped by Shahs. They won't do that. So not possible. She can't focus on the things she has. She should also join meditation classes but should not go for the same classes as Anuj. The problem with Anupamaa is that instead of learning, she will start teaching and then will distract everyone with her issues. A daily dose of drama will start happening in the mediation classes and will obstruct the well-being of other students too.. Perhaps she should become a jogan for real and not do pretense this time like the last time she did. 
Kinjal needs to leave Toshu and enjoy the luxuries of life her mother worked hard to earn for her. But she doesn't do that so even she can't be happy.
Adhik should get his daughter. Dimpy should file a complaint against Vanraj for restricting her movement and Kavya should leave the house. T2 for his own good should move away from the toxic house. Since none of them are doing what they are supposed to do in order to be happy. How can they be happy?
At the end of the day, no one has control over life's circumstances or what situations we might get stuck in. One can only work towards their happiness and make appropriate decisions. In this show, no one takes the initiative to be happy.
The bottom line is they can either take control of their lives and be happy or Vanraj Shah ALLOWS them to be happy. 