~さんどれにした? Gaijinian-san did this one already.
ちっこいけどいがいとおとな?
小さいけど、意外と大人? [The girl] is petite but actually mature (in thinking) to my surprise.
なんのおもて
なしもしませんが。
何のおもてなしもしませんが。 Omotenashi means hospitality, service, etc., to a guest. The sentence means "We can't do anything special/can't entertain you with special food, etc."
どうぞおあがりか?
あがる means to enter someone's house (coming from the fact that the floor level in a traditional home is one step higher than the ground level).
おまかいですが。
This one I don't know. Maybe something to do with the manga. I can't tell because I haven't read it.
A set phrase that reminds me of this is: お構(かま)いなく
This is used when you visit someone's house and you tell your host he/she doesn't have to do anything special for you.
~さんはきなすった ← 多分この文章「誰かは来た」って言うでも、どこ弁で書きましたか?
Dialect is called 方言(ほうげん)
I can't pinpoint the location, but I think it is used in the Kinki region (Nagoya is the largest city of this region), as well as many parts of Western Japan. I've heard it used in Hiroshima (my mother's home prefecture). Maybe Mikawa Ossan has heard it in his area (三河弁、みかわべん)
HTH!