Terraforming Mars is possible, just bloody expensive.
You don't need a core of rotating iron to create a planetary magnetic field. A coil of wire wrapped several times around the planet's equator and juiced up with many millions of amps would do it. Problem: cost. That would take several nuclear reactors, as well as the planetary infrastructure to wrap that many power lines around the entire planet's circumference. And that's just the magnetic field... a relatively minor luxury considering most early Mars colonies would likely be underground, but a necessity if you're going to eventually have plants and animals on the surface.
Heating Mars is conceptually easy, but hard to implement. Greenhouse gasses would work, but CO2 is a relatively inefficient greenhouse gas. A better greenhouse gas would be CFC. Yeah, it wrecks the ozone layer here on Earth, but in high enough concentrations, a CFC layer would effectively do what the ozone layer does here on Earth. What's more: each molecule of CFC traps as much heat as roughly 1000 molecules of CO2. Problem: cost. We'd need to spend hundreds of billions of dollars on factories to make CFC and ship it all to Mars... and that's not even including the cost of the equipment to ensure that no CFC accidentally leaks into the Earth's atmosphere!
Water may already exist on Mars, but not in abundances that would allow for a planetary ocean. Better to get water from somewhere else, like Ganymede or by intercepting small comets & having them impact Mars' surface. Either way, it'd take hundreds of years and trillions of dollars to give Mars an ocean. No ocean, no effective water cycle (unless you're using pumps and aqueducts & watering the plants on a planetary scale.)
...and none of that addresses the cost of actually putting people there!
You can't just print the money to pay for it. "Money's only paper." Yeah, but if you print enough money to pay for terraforming Mars, then you're also hyperinflating your nation into poverty. If you did that, inflation will make a loaf of bread cost $100,000 dollars, when the average citizen makes only $40,000 per year... if they're lucky!
All that said, I do believe Mars will be colonized and eventually terraformed. But it won't be the USA doing it in this century. It will happen gradually, over thousands of years. Barring some sci-fi breakthrough in transportation like teleporters or a warp drive, the first missions to Mars will be flags & footprints and they'll cost about $100 billion for each trip. The next missions will be tourists, after the LEO/Lunar tourist industry paves the way for cheaper access to space. The first actual colonists may arrive some time in the next century, but they'll be living underground and growing plants in specially protected greenhouses. No terraforming needed... at first. It's only when the population of Mars starts to grow substantially will anyone put money down on a terraformation project. That project may start as early as 2300... and even that's probably an optimistic estimate!
