I belive they are different years as on the Wikia there are 2 categories for First Year and Second Year Students
you'll notice that Akari, Chinatsu, Himawari and Sakurako are all first year students with Akari's profile on Wikiapedia saying that...
Chinatsu, Sakurako and Himawari are her classmates.
For Second Year Students we Ayano and Chitose however we don't see Yui or Kyoko on there but their character songs, but in the first years category Akari's and Chinatsu's character songs appeared here aswell.
Also in Yui's trivia section it says
Although she is arguably the most mature, she is the youngest of the Second-Year students.
While Kyoko is 25 days older
Oddly enough, as well as being best friends with Yui since they were very little, they were also born only 25 days apart.
also in this My Anime List forum post
Well, you know, I guess this is may be because of the difference of school cultures between Japan and Western countries, it seems translaters changed and translated from 'top in her grade' to 'top in her class'.
But actually, 'gakunen top' meant 'She always wins the top in her second grade'
Well, at any rate, just studying one night and getting such a high grade every time is so amazing.
while further down
In the US at least class generally refers to your grade level. When you refer to top of the class, that would be the top student of your year. Saying top of your grade is pretty much never used (I've never heard anyone use it personally). So that's a logical translation, it still means the same thing but is phrased appropriately for the US, which is CrunchyRoll's main target audience.
these are talking about what happened in Season 1 - Episode 2: The Student Council Meeting
Ayano, as Kyouko's rival, is upset that Kyouko beat her in the placement test. Ayano bursts into the Amusement Club room, followed by Chitose. Ayano is annoyed at Kyouko because although she hardy studies, she always gains top of the class.
Logically it would not make sense for Ayano, a Second Year, to be beaten by Kyoko if she was a first year.
Thus all this seems to indicate that Kyoko is a Second Year with Yui.
As for Akari not using -senpai to address Yui and Kyoko like what Chinatsu does this is probably as you suggest due to their closeness as later in the series
we see Akari, Yui and Kyoko as children when they were young with Kyoko being bullied by a young Chinatsu (who they don't recognize when they are older) and Akari standing up for Kyoko