Aspirin has a different mechanism compared to other NSAIDs and does in fact have well-studied benefit in heart disease protection and clot risk. That being said, that benefit is likely less than previously believed due to more recent studies and evidence and it does not come without risks, but it certainly exists.

In immunocompetent individuals it's unbelievably rare for a traditionally non-infectious cancer (i.e. all of them except the dog and Tasmanian devil ones) to be able to establish itself in another host, even if the cancer is directly implanted into the host. Part of the reason a natural/endogenous cancer can be so hard for the body to take care of is because it's composed of the host's own cells, which are obviously recognized as "self" and therefore less likely to come under attack by the immune system. Foreign cancers of course do not have this innate defense and so will almost always be very quickly killed off by the host's immune system.