The mix of leaky Relu at the first layers of CNN along with conventional Relu for object detection
how we end up with a model which uses a leak at the first layers and then a conventional RELU at the end?


What matters is to add a non-linearity to the outputs of a neuron. Consequently, by employing each function that adds non-linearity, the network will work due to the derivative that can backpropagate the differentiation of the error term. If you use Relu or leaky Relu, the update terms will change but your network will work fine. The reason that leaky version is used in the mentioned papers is due to avoiding dying relu problem which can happen a lot for regression problems. 

About your second question, consider that it usually suffice to use leaky relu in the first layers and due to them, the chance of deep neurons to be stuck at zero is not very much as the results of those papers show. You can use leaky version all over the network but by experience, relu is very fast to be trained!