Since E-Mobility is on the rise worldwide, large Charging Infrastructure (CI) networks are required to satisfy the upcoming Charging Demand (CD). Understanding this CD with its spatial and temporal uncertainties is important for grid operators to quantify the grid impact of Electric Vehicle integration and for Charging Station (CS) operators to assess long-term CI investments. Hence, we introduce an Agent-based E-Mobility Model assessing regional CI systems with their multi-directional interactions between CSs and vehicles. A Global Sensitivity Analysis (GSA) is applied to quantify the impact of 11 technical levers on 17 relevant charging system outputs. The GSA evaluates the E-Mobility integration in terms of grid impact, economic viability of CSs and Service Quality of the deployed Charging Infrastructure (SQCI). Based on this impact assessment we derive general guidelines for E-Mobility integration into regional systems. We found, inter alia, that CI policies should aim at allocating CSs across different types of locations to utilize cross-locational effects such as CSs at public locations affecting the charging peak in residential areas by up to 18%. Additionally, while improving the highway charging network is an effective lever to increase the SQCI in urban areas, public charging is an even stronger lever in rural areas.