This all seems engine related. It really needs a proper diagnosis by looking at all the sensor data, especially when it goes into a fault condition - otherwise you will be guessing. Worth checking that state of all the vacuum hoses in case they are perishing and open up when they get warm. It could be related to the MAF and O2 sensors, but you really want to narrow down what the problem is rather than throwing money at it by replacing parts that aren't faulty.
I don't think so. The faults related to hybrid are because the engine is failing to start - the same as those two new codes, they typically appear when other problems exist rather than being the root cause themselves. Worth checking you don't have water ingress in your boot though, as it is a common issue on older 400h vehicles.