I would recommend you post on Poland's Ancestry and Genforum boards. You really want your ancestor to be born in a little village around city of Warszawa and not city of Warszawa. You have few documents that say Warsaw, Poland? You located his arrival manifest and it says Warszawa/Warsaw?
Look over few sites for researchwww.rootsweb.com/~polwgw/index.htmlhttp://maxpages.com/polandwww.pgsa.orgwww.surnamenavigator.org
No surname BANDOSZEWSKI found in Poland. Do you know if this is slightly Americanized spelling to conform to pronounciation? http://say.expressivo.com
Distribution of ZAKRZEWSKI in Polandhttp://www.moikrewni.pl/mapa/kompletny/zakrzewski.html