There is a wide continuum from "cancer" in the sense of uncontrolled cell division (this could include even things like 2-3 extra cells making an imperceptible, microscopic bulge in your colon) to cancer in the sense of huge lumps of meat growing on your body and killing you painfully within X months. For the latter kind, many "stages" of "evolution" must be completed by "the cancer" (forgive the excessive quotes, but the terminology is a bit nuanced here). For a better idea of the nature of cancer, you could start by reading The Hallmarks of Cancer (and reading about it).
Which of the following is always present in the cell cycle?
There are eukaryotic cells like yeast which can be cultured in a medium containing only nutrients. Because these are unicellular organisms, there's no reason to expect that they have any growth factors or hormones or extrinsic signal like that (there's a caveat that often even unicellular organism can signal each other, but I believe there are also many that don't). All eukaryotic cells that divide have a cell cycle, so these cells also have it.
Therefore, hormones and growth factors cannot be required for the cell cycle. Cyclins and Cdks are a fundamental part of virtually any cell cycle ever seen by science, so you could say they are necessary (though I think it is conceivable that an organism could exist which progresses its cell cycle using proteins completely divergent from known cyclins and Cdks, but then again).
Which of the following is essential in cancer growth and division?
Without DNA replication, you obviously cannot make more cells, so that is necessary.
There are cancer kinds which are dependent on growth factors (perhaps they make their own growth factor) but there are also cancer which simply jam the receptor active, so that they can grow even without the factor. This is discussed in The Hallmarks of Cancer.
Signalling molecules (assuming that extracellular signaling is meant, because if you start taking away signalling molecules inside the cell like IP3, obviously you can break the cell to the point it won't divide) is just a superset of growth factors; same arguments apply because growth factors are the most potent "signalling molecules".
Control mechanism is also "obviously unnecessary" and "obviously necessary". Cancer is uncontrolled division, so if there was control, the cancer wouldn't be there in the first place, duh. But obviously cancer cells also control their own division to some extent - they still have a coherent cell cycle and so on.
Ultimately, the key to understanding cancer is being cognizant of "perspectives".
"The body" (actually the wild-type genome) has a certain plan in mind for what each cell should do, and to that end, it has programmed the cells here to divide so many times in so and so fashion and the cells there to not divide unless this event happens and so forth. If those cells are mutated, and that programming is disrupted, they may divide in ways the body "does not want" (ie. they create tissue which has not been evolutionary selected for over previous generations), so from the body's point of view the cancer is indeed out of control.
On the other hand, the cancer is almost like its own separate organism - for one, it certainly has a different DNA than you, as it has mutated. It undergoes Darwinian evolution and becomes gradually more adept at surviving and spreading inside your body. So from the cancer's point of view, the cancer cells are indeed quite well-controlled, with the goal of that control being to divide as much as possible.