It helps if you give more than one date of death or birth. Other data like who they married, other children they had, etc makes easier to help. However, based solely on when Michael died I was able to find the following. Hopefully it is the correct family, all of whom were in Pittsburgh.
Social Security Death Index: Michael Kitt, born May 1, 1901, died May 1970, last lived in Pittsburgh.
Andrew Kitt 58, widowed, born Galicia, Poland, speaks Ukrainian Mike 29 Katie 26 Paul 24 Ann 15 John 8 John Pelesi 25, nephew
Andy Kitt 47, born Austria, speaks Slovish, immigrated 1900 Mary 47, born Austria, speaks Slovish, immigrated 1902 Michael 18 Katie 17 John Pilese 16, step-son Paul Kitt 14 Annie 5
Andy Kidd 37, married 9 years, born Ruthenia, Austria, immigrated 1899 Mary 32, ditto, ditto, immigrated 1901 Mike 9 Kate 7 Paul 5 Frank 2
To be frank the place to start researching is in Pittsburgh. Michael's death certificate, obituary and marriage record would help to confirm his parents' names and also provide his mother's maiden name. The same is true of Andrew (probably originally Andreas or a similar form).
The PA Dept of Health would have the death certificates. Most likely they got their marriage licenses at the Allegheny County Register of Wills Office. The Western Pennsylvania Genealogical Society and the Historical Society of Western Pennsylvania might be able to help you with the obits.
The census indicates Andrew was a naturalized citizen. He probably applied for citizenship at the Allegheny County Prothonotary Office although he may have applied at a federal district court. His papers would probably indicate when and where he was born and arrived in the U.S.
I suspect Kitt was not his original surname although those who are more knowledgeable about Eastern European names can tell you much better than I can. Based on the census I imagine he came from the Carpathian Mountains in the area of or near Ruthenia which today is part of Ukraine, but borders Poland, Slovakia and Hungary.