Is it possible for someone to have leukemia and not anemia?

Yes. Depending on the type of leukemia, this is possible. For example, chronic lymphocytic leukemia is a slowly prgressive disease and it may take a while before the marrow becomes significantly involved to the point of affecting the red blood cells. Also, in the early stages of leukemia, anemia may not be present.
Yes. . It depends upon the rate of leukemia progression. If a leukemia developed rapidly, red cell mass may fall very little during that time, as the half life of a red cell is 100-120 days. Leukemias that evolve more slowly are more likely to have associated anemia, sometimes very severe. While not always true, slowly evolving leukemias often have a better prognosis because of their indolent nature.