1) Can I direct cable from the GPS/sounder to the laptop, or will I
need a multiplexer? I'm going to use an old IBM laptop that has two USB
and one 9-pin serial connections. Even if I can direct cable, will the
use of a multiplexer improve the ease of installation and/or the
stability of the connection?

You do not need a multiplexer to connect one single device to your computer.
The only benefit of using for instance a MiniPlex-Lite (3 inputs, one if
which can run at 38400 baud for AIS receivers) is that you have 2 spare
inputs for future expansion, it gives you galvanic isolation and it plugs
into your USB port while the supplied driver blocks Windows' Plug&Play
behaviour, so Windows does not see your GPS as a mouse (jumping cursor).

2) Can the setup be configured for the laptop to function as a second
screen replicating the GPS/sounder screen (similar to adding a second
monitor to a computer)?

No. The serial port only outputs GPS and sounder data, no screendumps. So if
you want somthing like this, you end up with option 3.

3) If the answer above to 2) is no, which PC-based chartplotting
program(s) will display the depth and speed from the sounder as an
overlay on the GPS navigation map on the laptop screen - or must I
toggle between two seperate screens on the laptop?

I don't know all the details of the various nav programs, but almost all
offer an extra window on top of the on-screen chart that shows data like
wind, speed, depth etc.

Meindert
www.shipmodul.com