How do we undangerize the radiation on Jupiter?
Since the question cannot be taken seriously the solution is to station gigantic fans above Jupiter and first blow away its atmosphere.
Which object emits more infrared radiation: the Sun or Jupiter? Why ?
It's sort of a trick question when you include that statement comparing Jupiter's emitted vs. received IR energy. Yes, Jupiter receives less IR energy from the sun than it emits, but after all, Jupiter is about 7.79E11 m away from the sun and has a radius of ~7.15E7 m, so it intercepts only about 8.4E-9 of sun's total emitted IR energy. (The ratio is calculated as that of the disk surface area of Jupiter to the surface area of a sphere of radius = Jupiter's distance.) So the sun actually emits ~1.2E8/1.6 = 7.5E7 times the IR power of Jupiter.
Why are Jupiter and Saturn so huge?
When the Sun formed it was surrounded by a disk of gas that consisted mainly of hydrogen and helium. The radiation of the Sun pushed these light gases outwards. They accumulated where Jupiter and Saturn are today, between 5 and 10 times the distance of the Earth to the Sun. Having so much matter available they could grow big.