DNA testing will almost answer your questions. However you must get a test that will show your latest DNA history. That means the last 200-300 years. It should be enough but you might not know where or exactly when the contribution to your overall DNA was added. A company called Crigenetics opened my eyes. Although my mother's family came from a town in Poland and had lived there for at least 300 years my DNA showed that I had among other things, Vietnamese DNA! Through research I found that my maternal Great Grandfather's father was born in Vietnam to a Polish Jewish male (my 3rd Great Grandfather) and a Vietnamese woman. Surprise! The boy was named Jacob, went back to Poland with his father and life went on. So I'm a Jew with Vietnamese DNA... so don't be surprised at anything!
Also test for your parent's Haplogroups. It will give you a larger albeit fuzzier picture.
It's a blessing to seek knowledge and a blessing to give knowledge.