A small centrifuge is not a viable place to have an entire colony to live in. Sure, you can stick someone in a high-g centrifuge by himself for a little while, but I'm talking about a habitat that people live indefinitely. Equating the two clearly shows you don't know what you're talking about.
> having a major engineering challenge due to the existing gravity?
Rotating a habitat is a hard problem in space or on a planet. But, Mars's is gravity would make the problem easier not harder. The atmosphere might be a problem, scale might be a problem etc etc, but gravity is not. Further, there may be little need for 24/7 1g, perhaps a tiny room to work out in is enough, perhaps you should sleep in 1g or perhaps 1/3 is enough for sleep etc.
But, again gravity is not the problem. And yes such a massive fundamental failure in understanding is a clear sign of incompetence.
Rotating something that size in Mars' gravity is far more difficult that rotating something in space. Clearly, you're far less competent than you think you are.