I really want to find a manga with some sort of social barrier. The most common being like a language barrier where the characters don't speak the same language and they have to like learn how to communicate. (I really love this stuff, also I have read Kanata Kara and watched Suisei no Galgantia) The second one I like would be like when someone doesn't understand like 'society' like how the main character in Noblesse doesn't understand machines or video games or ramen noodles. Stuff like that.
Thanks for your thoughts~

Hm, maybe try Pochi Kuro It's pretty fun. A human gets dropped into the demon world, and it turns out humans don't speak the same language as demons so she's totally lost as the demons who fished her out "take her in" to prep her as food.

You can check out the language barrier category.

Try Hataraku Maou-sama!, the light novel, anime or manga.
And it's more just for laughs in this case, but it's a commoner at an ultra-rich school-type situation. Not sure if it's exactly what you're looking for, but its entertaining.
Ouji ga Watashi o Akiramenai!

And maybe Safe Again Today

For your second request, I think Hinamatsuri and Alyosha! might fit.