The BRMFRSMG.EXE process (or service) is required by the Brother Resource Manager software. This software controls communication between the PC and the Brother device. If you stop this process your PC will not be able to communicate with the Brother device if it is connected via the Parallel or USB interface.
The BRSS01A.EXE and BRSVC01A.EXE processes are used by the Brother Print Processor (the Brother Print processor is an integral part of most Brother printer drivers). These processes run on a Windows® XP or a Windows Server™ 2003 environment. If you stop these processes your PC will not be able to communicate with the Brother device if it is connected via the Parallel, USB or network cable.