Although people may visit mars and enclosures might be build allowing a few scientists to stay on and explore mars for a few months or maybe several years, people can never live on mars. Mars is colder than the antarctic, dryer than the Sahara desert, no oxygen to breath, and almost no atmosphere.
Therefore,if humans are ever going to live places other than on earth, it is be necessary to travel at about one-tenth the speed of light. Otherwise, travel to the stars will take too long.
The so-called "light speed engine" isn't discussed in detail but appears to be an ion engine which has already been used on space probes. Ion engines are a significant improvement over chemical engines because the speed of the ions it ejects is far, far faster than the speed of chemical propellant, which means a far stronger thrust is enjoyed per unit of mass ejected. It does not violate any laws of physics. However, the amount of ions these engines can eject over time eject is, at present, tiny and quite inferior to chemical engines making acceleration quite slow so they are no good in braking during planetary reentry.
I was expecting something other than an ion engine to be discussed.
If it has carbon dioxide, it has oxygen as O2 is what CO2 is made of. Temps can be handled if there's sufficient energy sources. I'd expect bases on the moon or other planets to be underground as it aids in sheltering from solar radiation and add free strength due to pressure differences.
The biggest impediment to a permanent Mars presence is it's weak gravity. That will cause havoc on the human body over time. I suppose the space station has expanded our knowledge about that, but in spite of daily exercise, astronauts suffer bone loss due to the lack of gravity.
The only thing I've ever seen that violates the laws of physics -- biophysics in particular -- is how a woman can gain 4 pounds by eating 4 ounces of ice cream.
Yes, we're obviously a long way from terraforming tech that could let us make other planets habitable. Although here on earth, we have already started terraforming the earth by eating too much meat and driving SUVs.
The problem with Mars is too little gravity and Mars is too. Even if it was possible to dump an ocean of water and trillion of tons of oxygen on mars, it would be loss into space. I don't know how long it would last. Maybe millions of years. Even so it would still be too cold. Perhaps if you could add 80% oxygen and 20% CO2, Mars might be warm enough. However, while that would be good for plants, that much CO2 (about 600 times the percentage of CO2 in earth's atmosphere would be harmful to humans as even 10% would cause convulsions and death.