Great questions and I will try to answer. DNA testing does not tell you things like what country your ancestors came from. It does not remove the need for traditional book and record research. Instead, you use your DNA test results to focus your research to a paticular family group of people out of all the people in the world.
If your dad does a YDNA test, he will see a set of marker numbers and a haplogroup determined from a tiny bit of his DNA strand. The haplogroup is an indicator of where his ancient ancestors began thousands of years ago, long before there were surnames. The haplogroup will generally tell you if your ancient ancestors came from Africa, Asia, Scandanavia, Europe, etc.
Next, look at the marker results. If he has a match with another man in the FamilyTreeDNA database, those two men are genetically related. If they have the same last name, you may be able to determine which forefather was their common DNA ancestor with traditional research. If they have different surnames, their common DNA ancestor may have lived in a time before their surnames began. (They are genetic "cousins" but probably before there were searchable books and records.)
So, a yDNA test for your dad would certainly go back to his immigrant ancestor and millenia before. It would definitely show if his yDNA matches other men who have been YDNA tested and descend from the immigrant. Their yDNA will match exactly or closely. However, only book and record research will tell you which immigant brother you are related to.
In my own search, I traced my family back to the immigrant Joseph Smith, came forward on a different son's descendant branch from Joseph, and found an 8th cousin that agreed to YDNA test for our two branches. We fit in Joseph Smith's tree exactly as expected. Later on, a third cousin confirmed these results with his own test.
More on the next segment. . .