All three codes you mentioned are established subjects on this Forum and may be accessed using the Search feature. They may also be located via internet search engines, such as Google, using the query 'GM Diagnostic code ****'.
P0101 pertains to the Mass Air Flow sensor or air filter; P0700 is associated with the Transmission Control Module; P0796 concerns a transmission solenoid, often linked to automatic transmission vehicles. You did not provide enough car data to determine whether yours is automatic. This information is crucial to understand. If so, there is a significant likelihood of insufficient ATF (Automatic Transmission Fluid) or the fluid present in the 'box' is aged, degraded, and depleted. This may be impacting the gearbox solenoid (P0796); thus, I recommend having your technician replenish the gearbox fluid. If it has not been replaced since 2011, since there is no service history provided, consider having the whole gearbox cleansed and refilled. P0700 TCM may only be a 'sympathy' code produced by the ATF condition. The P0101 code, indicating a malfunction with the Mass Air Flow sensor or maybe a clogged air filter, can be readily rectified by cleaning or replacement. I see no direct correlation between P0101 and the other two, which pertain to transmission issues.
My comprehensive evaluation of P0101 and P0700 suggests that the car may possess a substandard service history.
To summarise, you may review the current conversations on all three codes by use the Forum Search feature. This will provide you with some context.
Secondly, kindly review your Sign-Up and finalise the sections regarding your World Location, which the Forum system identifies as the UK, and complete the vehicle details section (preferably the 'Footer' option) as it allows for more comprehensive information about the vehicle, including gearbox type, mileage, duration of ownership, and service history, among other details.