It is actually possible for microwaves to cause DNA damage. Because DNA is marginally thermally stable, intense heat produced by high intensity microwave radiation could reasonably cause DNA damage. Then again, the flame from a candle could also cause some DNA damage, so we better outlaw those too.

The end goal here is to activate the same class of CD8+ cytotoxic T cells that are specific for proteins expressed at abnormally high concentrations in cancer cells. Antibody based therapeutics for cancer are generally used to target radio isotopes to tumors which is completely different. There were however previous attempts to harvest T cells from the patient, activate them in the lab, and inject them back into the patient. The idea there was the same as here, but this seems to do a better job of activating the T cells, and at a lower cost. Also, it's not really an article on treating cancer. The original paper that the article referred to was "Infection-mimicking materials to program dendritic cells in situ," which appeared in Nature Materials, which isn't really a cancer research journal.

I think it could be possible. In the paper they described an implant that instructed dendritic cells to instruct T cells that recognize this type of tumor to become active and attack it. If I needed a heart transplant, it might be possible to make an implant that instructs T cells that recognize would recognize the foreign heart cells and attack them, to instead commit cellular suicide. That's pretty much the same way the body prevents the immune system from attacking it's own tissues anyway, except the process normally occurs in the thymus rather than a medical implant. The largest problem I can think of is that you would kill off a significant fraction of T cells would normally recognize the transplanted tissue. Even then though, it would probably work better than immunosuppressants.

There's a good reason they have to implant the device before injecting the cancer cells. The immune response isn't instantaneous, it takes some time, 2 weeks or so, for the immune system to reach it's full response. But this particular cancer kills untreated mice in about 20 days, which doesn't really leave the immune system much time to really do it's job. Fortunately, most types of cancer aren't lethal in 20 days, and for a more "normal" cancer that could take months or years to be fatal, the immune system would have more than enough time to fully respond. But, it's not really practical to use a slowly growing tumor for this kind of basic research. If you use a tumor that would kill the mouse in 6 months, it would just take too long.