Answering your two questions together, all cells enjoy many mechanisms that try to prevent the mutated ones from surviving. During the cell cycle of somatic and germinative cells, for example, there are three moments of verification in which the cell will undergo a kind of internal "check up". During the interphase, this process takes place between phases G1 and S and also at the end of phase G2. In the division, as soon as the interphase ends, there is also one more verification. If during one of these three steps any mutation is recognized, the cell will undergo apoptosis (regardless of whether the identified mutation(s) were in fact to induce a neoplasm in the tissue or not.

Now, if even with these three checks any or some mutations go unnoticed, the cell in question will go through cell division and the mutation(s) will be inherited by the new lineage that will follow; but this does not indicate that the cell will be cancerous, because for a cancer to develop it is necessary for specific mutations to occur in specific genes.

This was just some information I wanted to give you, now answering your question more directly: cancers as a whole enjoy very cunning mechanisms that aim both to make tumor cells indistinguishable from normal cells for the immune system as well as they try to make it very difficult for the many proteins of the Complementary System, which is a vital part of the recognition of abnormalities of the Immune System, to get closer. There are many mechanisms that tumor cells enjoy, but one that stands out is what is called the Malburg Effect. This effect, described by the German physician Otto Walburg, in the 20th century, in a simplified way, consists in the fact that cancer cells consume a much higher amount of glucose than healthy cells and still convert a good portion of this glucose into lactose. This considerable production of lactose makes the environment around the tumor or neoplastic tissue more acidic than usual, acidic enough to compromise the activity of the many proteins that play a role in recognizing abnormalities in the immune system. This is one of the many mechanisms that many cancers use, which, directly or indirectly, makes it difficult for the immune system to recognize it.

The Warburg Effect: How Does it Benefit Cancer Cells?
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4783224

Another interesting point is that of the five existing therapies to treat cancers currently (chemotherapy, immunotherapy, target therapy, hormone therapy and surgery), immunotherapy consists precisely in "training" the immune system to know how to differentiate a cancer cell from a healthy cell . In a very simplified way, what they do is surgically remove a slide of your tumor or neoplastic tissue, identify the proteins present in the cell membranes of the cells that make up the collected material (among other molecules) and differentiate what is there only in the tumor. From the moment the tumor's own molecules are identified, a kind of vaccine is made, in order to introduce a cocktail with these tumor-specific molecules into the patient's body so that the immune system can then chase the tumor cells, knowing how to differentiate of healthy cells.

Cancer Treatment Vaccines - Immunotherapy - National Cancer Institute
https://www.cancer.gov/about-cancer/treatment/types/immunotherapy/cancer-treatment-vaccines

There is also an explanatory video, if I'm not mistaken from Nature, very good to introduce the idea in a very general way of how immunotherapy and cancer vaccines work: https://youtu.be/jDdL2bMQXfE