1) You should be able to split/connect the NMEA0183 output from the Garmin to both the AIS and VHF with no problem, hence supplying GPS to both VHF and AIS. I would guess the VHF will limit the speed to 4800.
2) NMEA0183 is a 'single-talker' network, so you will need a multiplexer to get both DSC and AIS into a single
port to the Garmin. Also the multiplexer will need to support a 38400 input and a 4800 input, as I believe the AIS will be 38400 and the VHF 4800. Obviously, the output of the multiplexer will be 38400 into the Garmin. Since the port speed in #1 will need to be 4800 for the VHF, I don't know if Garmin can accept 38400 on the same port as transmitting 4800. This may be a show stopper for only consuming a single
port on the Garmin.
3) Although having DSC connected to your Garmin is useful, you will probably only see 1 or 2 messages a year on average. There is not much DSC traffic unless you buddy boat and use the position request/response mechanism.