To answer both:
1) When people say flight plan most think of the formal plan submitted before some flights. However, the definition of a Flight Plan is "Information to enable a flight or portion of a flight to be conducted iaw with an ATC clearance". Passing your details and requirements to the relevant Class 'D' ATC unit constitutes a "Flight Plan" as such.
2) According to the ANO you only require "Radio equipment capable of maintaining direct two-way communication with the appropriate aeronautical radio stations." One would be sufficient. However, you also however require VOR/ILS amd ADF. If the aircraft Comms / VOR/ ILS are not FM immune then you cannot fly IMC/IFR within CAS. (Schedule 5 of the ANO has all the details you need).