Jack is for Yaacov, Albert or Berah is for Avraham – some also use Alan, as for the others yes you are correct – they are nicknames, i used that version bec many dont use the full name, and i didnt know that ashkenazim also have them….
p.s. you’d be surprised by how many sefardim are named Jack.
as for israeli names dont forget – Guy, and Itai (i think they are boy names)also Yoram, Dudi, Uri