How could we establish a stable atmosphere on Mars without a sufficient magnetosphere to keep it safe from solar wind?

To establish a stable atmosphere on Mars safe from solar wind humans would need to use caves.

Caves of Mars Project - Wikipedia

Caves and other underground structures, including Martian lava tubes, canyon overhangs, and other Martian cavities would be potentially useful for manned missions, for they would provide considerable shielding from both the elements and intense solar radiation to which a Mars mission would expose astronauts. ...the "Essential Tasks" necessary for cave habitation are: finding extraterrestrial caves, protecting the scientific environment inside of a cave, dealing with the dark (providing lighting solutions for the interior of the habitats), cave life support.

The atmosphere which is needed for life would also be protected inside sealed sections of the caves.

The issue from the solar wind is one that matters over > 100,000 years, not short term.. if we can drop enough comets and shit onto Mars to give it a useable atmosphere, we can totally keep up on losses!

But where to get all that nitrogen? have to find the correct comets!

Now if you have air, you still cannot go outside in the day as the Rads will toast you somewhat.. no mag field!

What happens if the Federation discovers Earth, and Earth discovers they are being watched?

Earth would have minor panics before the Federation ensures that all of its technology is removed from the planet and leaves before it causes permanent damage to our natural path as stated in the Prime Directive. If it's the Earth from their past, they'd do

How far could Jupiter be from the Sun, and still be detectable from the Earth?

The hypothetical gas giant Tyche was believed by its proponents to orbit the Sun in the Oort cloud, at a distance of tenths of a light-year from the Sun. Data from the sensitive Wide-field Infrared Survey Explorer was used