Based off of dates shown in the manga/anime, the official yearly schedule for Seirin from KuroFes, and outside research on how Japanese schooling systems work. Plz note this may not be 100% accurate, but it’s my best/closest approximation based on the information I had.
For the day when Himuro and Murasakibara are introduced, I’m pretty unsure of this, but after some thinking I decided it makes the most sense for it to be in September. Seiho talks about preparing for exams (which would happen in October). The weather is still fairly nice/not very fall-like, which implies late summer to me and not quite yet October. Both Murasakibara and Himuro live quite far from Tokyo now (Akita is approximately ~4-ish hours away) so it wouldn’t make sense for Murasakibara and Himuro to just do a day trip unless they had time off from school. There’s the possibility they could have gone on a weekend, but Riko mentions specifically Seirin isn’t having practice “because it’s a holiday”. They don’t say which one, but there are no national holidays in Japan in October (except for Sports Day, but based on the KuroFes calander, this happens in Sept and not October for some reason like it does irl) but there are a few in September (in which most people have the day off from work/school) [these holidays are Respect for the Aged Day and Autumnal Equinox Day]. It would make sense to me that since Sports Day happens in Sept in knb (for whatever reason) that there’d be some sort of streetball tournament occurring on a national holiday dedicated to sports.
Nash and Jason’s ages are listed at 18 on the wiki, so I just chose to trust it even though I don’t think we’re given anything super specific for them (Riko and Hyuuga make a comment along the lines of “I can’t believe they’re not that much older than us”). So, if Nash and Jason are both 18 at the time of Extra/Last Game, that would mean that they’re in different grade levels, based on their birthdays and the enrollment cut-off dates of American schools. Both would also be out of high school (with Nash most likely having just graduated a few months before).
For more on ages in knb and how enrollment in Japanese schools works, please check out this previous post of mine.