The answer to your question depends completely on whether this node in the circuit is GFCI-protected. GFCI protection is an absolute must for your disposer; it's a high-amperage electric motor hooked up to your kitchen drain.
Since this J-box doesn't have a standard 3-prong outlet, you'll need to find another outlet on the same circuit; look for a countertop outlet nearby. Plug in an outlet tester (like the one below, available for $5-10 from your local big-box home improvement store), turn on the disposer, and hit the black button on the tester to short hot to ground, inducing a "ground fault".
If the disposer has GFCI protection, it will cut out, and you're golden as far as circuit safety. If not, you definitely need to rewire this J-box with a GFCI outlet.
Even if the disposer is GFCI protected, you have other problems. The outlet is in a "wet" place; you hope that the under-sink area never leaks, but there is always, always, a plumbing emergency at the kitchen sink at some point. To avoid a continuous ground fault through contact with standing water in the J-box (which would prevent you from resetting the GFCI until the whole area dried out), you should seal this area as best you can. A little adhesive spray foam to fill the gap between the wall and the back of the cabinet, followed by a layer of silicone adhesive caulk to waterproof the spray foam (people think spray foam is waterproof, but it really isn't), and a child-resistant outlet and plate with a rubber or neoprene gasket (and/or another dab of silicone) should keep the water out in any situation less than a full flood.
No, do not join all of the neutrals. The GFCI load terminals need the neutral to remain separate. Your diagram is correct in that respect.
However, kitchen outlets must be dedicated; the circuit may not be shared with lighting as you have in your diagram. This is almost certainly a code violation in any jurisdiction.
Best Answer
Just wire the GFCI between the wiring and the disposal so that it's on the switch (often, you would daisy chain the switch off of the GFCI and have the switched device hardwired, but that doesn't solve your problem). So, in your diagram, the load side is where the current is coming in, the line side goes to the switch, and the disposal is obvious. What you'll have is:
In the switch, the input is the white, even though it's hot in the wiring, and the output of the switch is black, since that's what becomes hot to the next device. When possible, I like to have my switch connected to a black and red wire, black always being hot, and red being switched. But that's usually not convenient, so this is the best an electrician can do.