I think you will be happier with separate vents. If you push air into one branch of a Y duct, it is going to come out of both of the other branches. That would push some air outside and some back toward the other bathroom. Even if there is a damper on the fan so that most of the air couldn't actually get into the bathroom, it will cause turbulence at the Y and make each fan slightly less efficient. The best design for any venting is always the simplest. Just keep the run as short and as straight as possible. The fewer complications you put between the fan and the outside, the better the system will work.

"...there are only 2 black wires, and 1 copper wire (ground). The instructions say i have to hook up the white wire to a set of white wires in the junction box. but there are no white wires in the junction box." I'm a bit confused by this description. Did you mean that there are 2 black wires, 1 copper wire and 1 white wire?. That's what would make sense. Assuming that's the case, here's the deal: There are a couple of ways switches can be wired. One way is that the power feed first enters the switch box with both a hot (black) and neutral (white). The neutral is simply passed on to the fixture (i.e., the incoming white is connected to the outgoing white). The incoming hot connects to the switch and an outgoing hot goes to the fixture. (So, two wires in, two wire out, right?) A second way is that the power feed goes first to the fixture. The white (neutral) connects directly to the fixture and the incoming hot goes to switch along with what we'll call a "return" wire. This is known as a "switch loop" and it has no neutral. One wire is "always hot" (the feed) and the other is the "switched hot" because it only gets power when the switch is on. [There are a couple of other ways to wire a switch, but these two are the most common.] A simple switch does not consume power itself. It only connects the two wires then it is closed ("on") and disconnects the two when it is open ("off"). The problem arises when a more complicated switch needs power for something. For example, a switch with a pilot light or night light consumes power itself and so it needs a neutral. Ditto with some timers. You cannot wire a switch that is itself a power consumer to a simple switch loop, which is apparently what you have. So, there are two possible solutions. First is to do some rewiring to bring a neutral into the box. One way to do this is replace the switch loop cable (two wires) with a three-wire cable, one of which will connect to the neutral at the fixture. Since you're not familiar with wiring, I won't elaborate on how to do this, or other ways this can be accomplished. You'd probably need an electrician. A second possible solution is to find an old-fashion mechanical timer that doesn't use electrical power itself. (It's basically a switch with a "wind up" spring.) This assumes, of course, that your intended purpose is just to let the fan run for a while and then switch off by itself. If your objectives are more sophisticated than that, I'm afraid you're SOL. Good luck.

The main reason is laziness and cost. What they should have done is installed an insulated 4 inch flexible duct to a capped roof vent. It needs to be insulated so the warm air does not condense in the winter and drip into the fan. Your old fan probably got rusty because there was no roof cap and the duct was not insulated.

What you have chosen are good selections. We have never gone wrong specifying Panasonic fans for our clients.