If I want to make a communication satellite, like MarCO, what formulas do I need to calculate the perfect antenna? Is there a difference between the X-Band and the classic UHF? If the cubesat is destined for some saturn moon, does it have to have a larger antenna due to the interference of its other moons? How do I receive the antenna information?
There are too many general questions here that require book-chapter-length-like answers. I would like to specify first:
Do you want to calculate antenna performance, antenna pattern, or what exactly? Additionally, which antenna do you have in mind: ground station antenna for an uplink scenario, antenna on-board of the CubeSat for a downlink? In terms of performance, I would suggest to look for such calculation generalization as a link budget, as by calculating solely the antenna performance you won't be able to say if you can successfully close the link with your planned CubeSat. There are tons of examples in Internet and scientific publications, thus I advise you to review those first. For instance, this presentation will give you a good feeling what link budget is.
There is, of course, difference between bands. X-band is a frequency band between 7 to 11.2 GHz, while UHF is between 300 MHz and 1 GHz. In terms what frequency suits your mission in a best way, it is again quite broad question. It really breaks down to the mission requirements and subjected towards thorough trade-off analysis.
Larger antennas on CubeSats (and satellites in general) are nothing to do with interference. The main advantage of a larger antenna (let's assume parabolic reflector) is the larger gain. What is gain? See here.
You, of course, can do some engineering assumptions regarding your antenna when doing your link budget calculations. However, without prior knowledge of state-of-the-art or specific antenna device in mind, it is a hard task. Considering the desired deep-space scenario, I would recommend you to do a thorough literature research, check the flight heritage of successful missions, what kind of communication strategies they used. Having the previous experiences in mind, you can start an iteration process where you combine all the elements of your communication scenario into a link budget calc and see what kind of resources would you need to successfully close the link. This process would take a while, as it is considered to be a compromise between the desired performance, available power resources and current state of the technology.
But again, I advise you to make some effort and provide us with some rather more specific questions. So far there are so many ambiguities in your question that you cannot expect anyone would provide you with precise answer.