There are several issues with this family that require broad thinking. 1) Name variations - Gaca,Gazca, Gacza, Gatza, Gotsa, etc. 2) Birthplace- The area often referred to as Poland was at various times part of Germany and at other times part of Russia. 3)Ages and immigration dates often vary based on the knowledge/accuracy of the person providing the information and the accuracy of the enumerator (and sometimes the transcriber, when no original document is available.)
Immigration - Ellis Island Alexander Gaca, age 24,arrived 5/29/1906 sailing from Bremen-going to Brother, Waclaw Gaca-Duquesne, PA.
Fortunately Waclaw applied for a passport in 1920 to visit his mother & sister in Danzig.Says his father's name was Frank Gaza.He references a letter from his mother and sister imploring his visit, which is necessary as all sons are in the army or in the US.Waclaw was a grocer in Pittsburgh.-Passport app. can be viewed @ ancestry.com (includes photo)
Although parts of this don't match up, I'm 95% certain this is your family-
1920 W.1 Duquesne,Allegheny, PA - Jan. 11 Gotsa, Aleck 38 Poland steel laborer imm 1905 alien Mary 26 Poland imm 1907 alien Max 7 PA Joseph 6 PA Gustav 4 11/12 PA Virginia 3 1/12 PA Adam 1/12 PA
In the old country, christian names and given/common names were often different.The only place you will usually find both is in church records.
There are two other Gaca/Gazca/Gacza families in Duquesne, that I suspect are also brothers to Alex and Waclaw.Frank Gaca and wife Romania/Petrona; and Joseph Gaca and wife Frances.