You and I corresponded a bit about 20 months ago...Here's the only bit of additional information I have, courtesy of Helen Hinchliff's "Tracing the Mumper Trail #5 - Twentieth Century Immigrants": Peter (age 23) and Katalin (Katharina Rothgerber - age 17) departed Coxhaven, being originally from Csatad, Hungary, on 29 Feb 1908 on the SS Amerika. Helen writes the record shows Peter's father as a Sebastian Mumper of Csatad. They were met by Peter's cousin Sebastian Schicker. Peter was described as 5'-5", fair complexion, fair hair, grey eyes.
Katharina was 5'-4", fair/fair/grey. She is also shown as returning to Csatad in 1911 and entering the country again in 1912, in the company of her sister(?) Anna Kucsara.
Alas, that's all I have, though if you want to get in touch with Helen, you may do so through the Mumper Family Website, for which an invitation is on the way. Your father was interviewed by Helen back in 1989, and was profiled in issue #4 of "Tracing the Mumper Trail".