In this paper, we exploit an emergency mobile crowdsensing (MCS) framework that utilizes unmanned aerial vehicles (UAVs) in collaboration with uncrashed base stations (BSs) to enhance sensing and communication efficiency. In the proposed framework, mobile users (MUs) equipped with sensors collect data, while UAVs, deployed as aerial relays, collaborate with uncrushed BSs to facilitate the transmission and aggregation of the sensed data from all MUs. However, the limited resources significantly affect the deployment of UAVs and the design of the UAV-relay-assisted MCS system. Moreover, selecting MUs for sensing tasks and allocating bandwidth among them are crucial factors that determine MUs' sensing capabilities and the data transmitting policies. Incorporating with foregoing essential factors, we formulate a comprehensive problem that jointly optimizes the MU selection, bandwidth allocation, UAV deployment, as well as strategies for sensing and transmitting data, aiming to improve the total reward of agent. The formulated problem poses high challenges due to the coupling between the sensing, transmission, as well as the UAVs deployment policies. To deal with this problem, we first derive the optimal transmission power and sensing data size under given MU selection, bandwidth allocation, and UAVs deployment strategy. The original optimization problem is subsequently decomposed into three folds, corresponding to finding the optimal MU selection, bandwidth allocation solution, as well as the deployment of UAVs. Meanwhile, a joint dynamic programming and a swap-then-compare enabled algorithm is proposed to obtain the optimal MU selection and bandwidth allocation policies. Next, the successive convex approximation (SCA) techniques are used to find the optimal locations for the UAVs. Extensive numerical results verify that the proposed joint algorithm can significantly outperform several benchmark approaches.