P0410 is the secondary AIR pump - that system which sends fresh air to the exhaust manifolds at cold start in order to quickly light off the cat. The assembly is in the left front fenderwell, inside the plastic liner and it feeds the two AIR valves - one on top of the rear cam cover, the other down by the water pump cover (lower driver's side).
U codes are voltage and data transmission hiccups. Is this code Current or History ?? If it's H, don't worry about it.
B0429 is the diverter door or actuator for air to the rear console panel. If the rear console controls work, the fan runs at its 3 speeds and there's airflow, don't sweat it. Otherwise, remove the glove box and passenger side under-dash and kick (left) panels and troubleshoot the actuator.
www.alldatadiy.com if you don't have a real GM/Helm Service Manual (Haynes and Chilton are useless - far too generic).
Ignore the U codes unless you are having some sort of problems.
B0429 is common and just means that the rear temperature actuator is not in the commanded position. I've been told it does not take much so unless you are having a problem controlling the rear seat temperature, ignore that too.
Neither of these codes is causing a Service Engine Soon light. That was caused by P0410 & should have gone out when you replaced the AIR system pump. You can check your DTCs and see if P0410 is gone or at least now listed as "H" for history.
You can search for code B0429 on here - it is fairly common & is only of any importance if your climate control isn't working right, otherwise can be ignored.
U codes come & go on these cars and are usually of no significance. Wait and see if it goes away on its own.
Edit: sorry Sub & Ranger - you both must type faster than me.