No, it's a good sentence. :)

It is not that unusual. Especially when there is an adjective in-between. It is completely normal like this.
If we omitted "A", the word "kis" could easily be mistaken for Éva's "last name". Family name comes first in Hungarian. "Kis Éva" is a complete Hungarian name.

Not wrong, just focusing on the girl rather than on what she's doing.