is the te-form of the verb + (), the subsidiary verb () . It's used for "went (and came back)" or "have (just) been to", e.g.
> I've just been to the post office.
* * *
> []{}[]{}[]{}[]{}[]{}
It literally says "Today, I went to the sparrow's house, saw delicious dishes and sparrow dance, and came back." (The []{} here is not inn but house; when ojiisan sings "suzume, suzume, oyado wa dokoda?" he's looking for the little sparrow's house, not their inn.)
But as you can see, the writer intended to say "Today, I went to the sparrow's house, ate delicious dishes, saw sparrow dance, and came back."
I'm not sure this is grammatically "correct" (actually I think it's probably sloppy/wrong) but, we often say and hear sentences like this in daily conversation, or sometimes even in tv drama:
> * I drank bread and coffee for breakfast, and...
> * I ate juice and cake for snack.
> *
>