I think the most possible time frame of Season 1 is mid August (Star Comes to Earth) to mid October (October 16 to 20 maybe? Storm the Castle) Mid August because Star came to Earth when Marco was in school and the earliest time frame for summer vacation in the USA is late May to early August which also works nicely with the whole "Beach day" thing and Marco being clearly somewhat ok with being in highschool. Mid October because for a fact, Storm the Castle has happened before Hungry Larry (Oct 31st) (look at the wand it has a yellow heart at the bottom and the wings of the wand are pointed up unlike the full Season 1 wand with a blue heart and wings pointing straight out) which also works well with Star befriending Janna after Storm the Castle in Girl's Days Out so she's in Hungry Larry to begin with. I mean this probably means Season 1 episodes don't occur in chronological order as they came out tho.

Also no, the Blood Moon Ball by going off of real life would be October 8th, 2014 (which is a Wednesday and guess how we start out that episode? At school) due to Star still having her wand.