That's an easy one. We've discussed this before, and the Sheet Music is at The Lester S. Levy Collection of Sheet Music SWEET EVELINA. As to authorship, all I have EVER found, including asking scholars who would know if ANYONE knew, was Words by M., Melody by T. That is likely the best anyone is ever going to do since it was published in 1863.
To find the earlier discussions, just put Evelina in the search box. Evalina might pull you up some threads, too.