I would like to do a run of this game but I’m not able to complete it in one day and I was wondering if you had to complete the whole game in 1 session or if you could take multiple days to finish it

RTA speedruns (which are the standard in the speedrunning community) are always done in one sitting, with the same timer going from the very start to the very end. You could split your run up into 120 stars one day and green stars another day though, since it would basically be a 100% run and you can "add your times together" to get the true 100% time (kind of). Although you would not be able to submit it as such.

Yes. You can, however, sleep and put the final total time after, like April did with her 14 hour TA/23 hour RTA speedrun. https://www.speedrun.com/smgalaxy2/run/y975lvkm