Finding Maria's and Jakim's church marriage record and the sons' baptismal would answer some questions.
I suppose Maria and Jakim already knew English as "Russian" and Slovak are not the same even though they are Slavic languages .
Go from known to the unknown. Have you considered requesting your grandfather's SS-5Form? It would give you his place of birth.
Have you found Jakim's Draft Registration Form at all? You would need Jakim's Death Certificate to request his SS-5Form.
Being that Maria SESTINA was born in what is present Slovakia/Slovak Republic, I would recommend posting on that country's board. Some of the regulars surely will find her parents marriage.
Which is the Jakim's arrival manifest you say I found?
Did Jakim have a sibling, uncle or a cousin that he came to stay with?
Szuhan, Maria Rochfalva 30 1869-1870 1900
She is going to cousin And. TELECKY in Export, PA.
Telecski, Matyas Rokfalu 25 1876-1877 1902
Fereski, Gyorgy Rokfalu 32 1868-1869 1901
Foloczki, Georg Rokfalu 33 1868-1869 1902
Szesztma, Andras Rokfaln 26 1875-1876 1902
SZESZTINA on the manifest. going to Siegfried, PA to br.i.l. Andras ADAM.
Adamo, Maria Rokfalva 21 1880-1881 1902
Adamo, Maria Rokfalva 1 1900-1901 1902
Second trip for Andras.
Szesztina, Andras Rodwezy 26 1876-1877 1903