It is a rechargeable battery and comes with a USB-C charging cable, but no adapter. 

This projector doesn't have a built-in battery, but they provided a power adapter in the package. 

yes, the flash can work on Canon 7D 

FD-EOS fit for Canon FD mount lens and canon EF mount camera body. canon 60d is EF mount, so the adapter ring can work with your camera, but you need to check your lens mount. could you pls let us know your lens specific model? service(AT)kentfaith(DO NOT)com, Please note: It is not same between Canon FD mount and EF mount, this adapter ring is only for Canon FD mount lens, please contact us if you want to purchase for Canon EF mount lens. 

1. Canon DSLR mount(Canon DSLRs, e.g. Rebel Series, 700D 650D 600D 550D 7D 60D 7D etc) is called EF, usually expressed by EOS, and Canon mirrorless camera(Canon EOS-M mirrorless cameras like M1 M2 M3) was usually expressed by EOS M
2. Nikon DSLR mount(Nikon DSLRs, e.g. D40 D70 D3100 D3200 D3300 D5100 D5200 D5100 D7100 etc) is called AI or F, usually expressed by Nikon/AI, and Nikon mirrorless camera(Nikon 1 series mirrorless cameras like N1 1 V1 V2 V3 S1 S2 J1 J2 J3 J4 AW1 ect) was usually expressed by Nikon1