I have bilateral carpal tunnel syndrome, also c5-6 pinched nerve, will carpal tunnel surgery lessen the pain and numbness and tingling?

EMG/NCV. I suggest you get a emg/ncv study (if you have had symptoms more than 3 months) to determine if you have carpal tunnel syndrome and/or c5/6 radiculopathy. This is the best way of determining your actual diagnosis and not a steroid injection. Good luck.
Yes. When you have a double crush, relieving one area of compression will help. A great test to see how much it would help would be to try a steroid injection in the carpal tunnel first.
Unclear diagnosis. Clinically a cervical radiculopathy (pinched nerve) at wither c5 or c6 levels should be distinguishable from the symptoms of cts. A well done EMG and ncs should help you confirm the diagnosis, quantify the extent of nerve injury, and qualify the type of injury (conduction block, denervation, etc.). I would not proceed to surgery under these circumstances without a more accurate diagnosis.
It might. Carpal tunnel surgery will likely make your numbness better. However, you may continue to have residual numbness and tingling in the hand due to the c5-6 nerve compression (aka cervical radiculopathy). Because you have what is known as a "double crush phenomenon, " release of the carpal tunnel may be helpful to improve your overall clinical picture.
Carpal . Tunnel affects a different part of the hand or arm than a c56 lesion. If you have classic cts hand symptoms and a positive ncv/emg for carpal tunnel then you should expect a carpal tunnel release to help . If there is more cervical involvement. Then the EMG indicates it may blunt your response but typically i'm the scenario you mention i'd tell someone to go have the ctr.
Depends... Other docs have addressed this question, but i'd like to suggest (assuming you already have emg/ncs proof of both conditions) the least invasive thing first: 1) carpal tunnel steroid injection. If this helps with everything, great, maybe get surgery in future. 2) cervical epidurals: if this eliminates all pain, great. Better/easier to get a carpal tunnel release than a cervical discectomy.
May. Some of your symptoms are related to nerve damage at cervical level and some to carpal tunnel. Only your physician can advice you, because he had the privilege to examine your records. You always can get evaluation by neurosurgeon who can address both problems. Did you have EMG study?