But anyways if you can set a permanent base in Arctanctica, setting one in Mars shouldn't be an issue (apart from getting stuff to Mars )
Mars would not be impossible either, but it would be a lot harder.
Apart from getting materials to Mars, there would be problems with food and water supplies. And of course, we must not forget the problem with oxygen. And the risk of meteor crashes is much higher thanks to its thin atmosphere. Oh, the atmosphere would also be a big problem since it doesn't stop much of the cosmic radiation. So simply, it would be a LOT harder.
So, lets not mix apples and pears, shall we?
It is impossible, 6 month of night during polar winter at -70°C with nothing that can give you supply, you'll need a closed heated ecosystem to grow you own food which requires tons of energy
You can grow food on Mars and water is abundant on Mars and you can create a micro ecosystem CO2 is abundant in Mars plants will creat oxygene trough photosynthesis as there is abundant sunlight you just a green house to creat decent pressure, and yes you'll need space suite on Mars but you can creat oxygen being trough plants or water and air recycling and co2, as for meteorite, earth has more gravity and thus it is bound to attract more meteorites than Mars, also Atmosphere only burn small meteorites while for big ones it either makes them explode or split which is more devastating as for cosmic radiation is a non issue if the habitat is underground
You can grow food on mars, and there is water there as well. But you'd still need energy to heat it up. Remember that it can be as cold as −153 °C during night times.
Earth may attract more meteorites than mars, but the martian atmosphere is a lot thiner than the earths.
And basically you're just copying my plan, but instead want to apply it on mars.
It would be much easier to build it on earth. Also, if we fuck up on our colony, we'll get help from the outside world. You won't.
Also, the gravity is much lower on Mars, and we don't know how the effects on the human body in such low gravity long term.
-153°C is the minimum temperature registered on Mars, it doesn't mean it gets that cold everywhere, in the equater the trempreture is more earth like that you might think.
This was answered, Atmosphere when it comes to meteorites won't make much difference, earth attract more and gives more kinetic energy to the incoming meteorites, and since we observe Mars and had probes and orbiters around it there was way more meteorites that impacted earth than on Mars.
Copying your plan? I didn't even read it, but as you mentioned your plan has some issues, like the soil on Artanctica is 4km deep and to how deep you think you need your base to be built under to be adiabatic? how much would it cost? as for Mars just use an available cave, or use a 3D printer if you don't want to dig to built your own habitat, this plan was presented 3 decades ago by Dr Robert Zubrin, he didn't just present Ideas, but a whole plan presenting everything, from risk to cost. so no not copying your plan.
Getting to Mars and getting the material needed to Mars is the biggest problem in the equation, while when it comes to Artanctica that's a none issue, yet why there isn't a permanent scientific station to this day? while scientist runs whenever it is winter, the scientific research there is of such importance, from meteorological studies and ozone hole studies to, underground sealed lakes like the Vostok and what's not, (btw scientist had to leave because of winter just at the edge of it !)
As for gravity it's not much lower it is indeed lower but we aren't talking about the moon here we are talking about Mars which has around 38% of earth Gravity, which is easily negated with the heavy space suites, Gravity would be a problem getting to Mars on zero gravity not being there in a lower gravity that you can negate the effect.
Like I said before building a an a floating Island in international water is the most possible and cheapest plan to do