I was actually kind of surprised that Yamada took so readily to calling the new girl by her first name. She doesn't even call Mikawacchi by her first name, nor vice versa, and they've known each other the longest. It just seems kinda...out-of-character for the straight-laced Yamada. I wonder if this is going to be a plot point.
In the case of Mikawa (and Kase for that matter), Yamada probably learned her family name first from a class introduction or something before they really became friends, and vice versa, so that's just how they started calling each other and it sort of got ingrained, so they likely just stick with that because as Yamada says it would feel weird for a while to change it.
In the case of Hana, she just flat out tells Yamada when they first get introduced to call her by her first name so she did (plus Hana is the kind of name flower loving Yamada would like anyway) and reciprocates.
As for Kase's reaction to the lipstick, I think there's a few factors at play here - as noted Kase had a similar hang-up over Yamada wearing an apron at the school so we have some precedent. Plus she's already uncomfortable being at this fancy cafe plus she found out that Yamada made a new friend she's already on a first name basis with plus Yamada's really happy getting a gift from Mikawa PLUS Yamada is talking about how all the cool girls at her school are wearing makeup and thinks she should too. All of that is kind of a perfect storm for kicking up Kase's already latent jealousy over Yamada to the max. That doesn't excuse Kase, but it does explain her extreme behaviour some.