I presume you fractured your patella?
After this sort of surgery you should get physiotherapy. the patella is part of the mechanism of the quadriceps muscle that controls your knee. The quadriceps muscle is the very big muscle in the front of your thigh. The patella is continuous with the muscle and acts as part of a pulley mechanism that straightens your knee. When it is damaged the whole pulley mechanism is affected. Following the imobilisation after the surgery the mechanism becomes stiff due to the swelling and inflammation around the fracture and surgery. the quadriceps muscle can't work properly and it becomes weak.
In contrast undergoing rehabilitation where the various parts of the pulley mechanism are strengthened and stimulated to work properly well help get a better result.
You really should be getting advice from your surgeon and a physiotherapist.
this is usually due to the immobilisation and damage to the joint surface of the patella. The muscle may also have lost it's normally length . these factors can stop the knee bending properly1) I can't bend my knee completely, can i be able to do it completely ?
Most likely this is due to the imobilisation and the swelling. the swollen tissues can lay down scar tissue that can make matters worse. Physiotherapy can help to mobilise the patella and improve the pulley action of the muscle. Whether or not it will ever be normal depends on how bad the break was and how good the surgery is but rehabilitation will usually help a lot.2) My left patella and skin around it is still stiff, will it become normal ?
This is a critical time to get help. the bone should have healed so the knee should be ready for physiotherapy. Delaying treatment could result in a poorer outcome3) I haven't been taking any physio classes, doing exercises on my own, is it ok ?
This is the sort of thing you need to get advice on. Without a proper assessment of your knee I wouldn't want to give you advice.4) I'm climbing stairs can i continue ?
these would make good goals in rehabilitation to work towards. Usually you need to work up to these things and a programme of mobilisation and strengthening may help you get there.5) Can I play cricket, badminton as before ?
Please don't ask advice on specific exercises. You need to consult a well qualified physiotherapist who can properly examine your knee and is aware of the surgery you have undergone.. The physio should consult with your surgeon on the best approach to take.