It is neither too hot nor too humid in early June in Beijing, you may get more information from Beijing Weather(https://www.travelchinaguide.com/climate/beijing.htm). There are many Muslim restaurants in Beijing(https://www.travelchinaguide.com/cityguides/beijing/dinning/muslim.htm), of which there are some featured ones like Hongbinlou at No.11 Zhanlan Road of Xicheng District, Kaorouyuan at No.58 Nanlishi Road of Xicheng District, Youyishun at No.28 huangsi street of Xicheng District, Donglaishun at No.63 of guanganmen neidajie, Jubaoyuan at No.1 business building Niujiexili of Xuanwu District and wangdelou at No. 26 dianmen waidajie of Xicheng District.