BMW Differential Carrier Bushing - Whiteline KDT919

Is this a complete differential mount kit?

Yes, it is.

I have a 2011 335i w/ M Sport package. I am doing a complete suspension refresh. I have already purchased the M3 control arm kit, Eibach sway bars, new sway bar links, new coil springs, new shocks and struts. I am also going to purchase the Revshift trailing arms and new bushings. Would it be a good idea to replace the rear subframe bushings and the differential bushings?

Considering you're doing major suspension upgrades intended to "tighten up" the rear end of the car by reducing unwanted movement it's not a bad idea to focus on the main connection between the chassis and the suspension which would be the subframe mounts. The factory mounts used on the non-M cars focus more on reducing NVH (noise, vibration, hardness) and you'll be surprised how much deflection/movement the rear subframe has under load. There are a lot of options to deal with this including poly subframe bushing inserts or upgraded sunframe mounts (M3, polyurethane, or aluminum). When it comes to the differential mounts we find they are somewhat less of a critical performance item but more of a maintenance item. Generally, the M3 subframe mounts are a reasonable enough upgrade.

My car has been developing a clunky noise that only happens when I initially accelerate and decelerate. It sounds as if a water jug is rolling back and forth in my trunk. It's slowly been getting louder. Would this probably be the correct replacement part

It's a possibility that it could be worn differential mounts but would also check the shock mounts as well.