I took a DNA test and it says 25% Ashkenazi Jewish so many unanswered questions?

You're conflating "Jewish DNA" with "being Jewish." Jews have stayed so tight-knit for so long, they have their own distinct genetic haplogroup, so you may have 25% Jewish DNA, but that's just your ethnic and genetic background. When you refer to the maternal descent, that is more to do with the Jewish community accepting somebody as a Jewish person under Rabbinical law, i.e., religion, e.g., having the right of return, etc. Just having DNA that is shared with Jewish haplogroups doesn't make you "Jewish" you have to actually be accepted by the Jewish religious community to be considered "Jewish" in that sense. I also have Jewish ancestry, but like you mine is on my father's side. My DNA tests have come up all over the place. On one test it said I had only a tiny sliver of Ashkenazi and then some Middle East, Caucuses and Eastern European adding up to around 4% total. And on another test, for my Jewish, I think it turned into Sephardic, Greek, Slavic and Southern European adding up to about 8% with these groups all combined on that one. Mine is from a great grandmother on my dad's side, so I guess their algorithms had to do a little more guesswork, but I know I am not Greek, Slavic, or Southern European (which is Spanish/Italian I think mostly), so that must have been something that the other company's test might have combined together to put all in the Ashkenazic and Middle East, Caucuses, Eastern European and mixed in some of my German in there instead as I got high Western Europe but most of my German comes from my Jewish side (They were Jews from Trier), but it broke it all up into totally different population chunks in this other test, so make with that what you will, they're all doing a lot of guesswork I think, and you just kind of have to understand they're not the gospel. They rely on estimates and presumptions that can go in multiple population groups sometimes. My cousins who took test on same company where my Jewish came up as Ashkenazi, who share our same Jewish great grandmother all got around 6% Ashkenazi though, so not sure why their's came up so concise and not mine. My great aunt, the daughter of a Jewish mother, only got a small amount of Jewish too (but she only took the test on the company where mine came up as Sephardic) but she had really high Eastern and Southern European, which I know she has none of since she would have the same ancestry as my grandfather, so I don't know what that test was doing. My overall DNA profile must have confused the algorithms, as I have a lot of Dutch and English and Scandinavian, whereas my second cousins have a lot more Italian and Southern European stuff, but still not sure why my great aunt came up so wrong on the one test as at least one of her grandchildren on the other test came up with more Jewish than her. I mean, she should have had 50%, and me 12.5%, so who knows. And I am also not sure if what we got from our other sides of our families made a difference or I just didn't inherit as much DNA from my Jewish great grandmother or what, as my actual definitive "Ashkenazi" or "Sephardic" results on either tests were only between 1-2% but then got all these random other things I have no evidence of in my family tree for that has over 40,000 people on it. I swear they just throw darts at a dartboard or something, because I know my great aunt claims her mother was Jewish and that her Jewish family came from Trier. And I think she would know what her own mother was.

And when I researched this, it said that the groups that I got that I have no evidence in my family tree for, all happen to be commonly found for Ashkenazic Jews also and share a lot of commonality with their DNA with those groups. This makes sense, as they did migrate from the Levant area and went through all those places into Europe. Here's a Wikipedia article talking all about it, so maybe it can answer your questions. https://en.wikipedia.org/wiki/Genetic_studies_on_J...

Please read your bible. It explains what happened to the Jews. 

Jews as an ethnicity are divided into Sephardic (roots to Spain), Ashkenazi (eastern Europe) and Kazar, a group which converted to Judaism around seven or eight centuries ago.  If your DNA check can be believed, one of your grandparents came from somewhere in eastern Europe, and was of Jewish parentage.

Jewish is both a religion and an ethnicity. The Jews in what is now Israel and Palestine were driven out of their homeland in 70 AD by the Romans. Many, not all, of them went to Europe. Some of them or their descendants inter-married with Europeans.

Read lots more:

https://en.wikipedia.org/wiki/Jewish_diaspora

It is possible to be 

Ethnically Jewish but not religiously;

Religiously Jewish but not ethnically;

Jewish in both religion and ethnicity.

"Are these European Jewish people technically Israeli people who migrated to Europe"

Nope, they're European not semetic.

Judaism is a religion.  Being Jewish may be seen as a religion or an ethnicity; and in the case of DNA, it involves having the genetic traits common in that ethnicity.

Throughout history, most Jews did pass their religion down to their children.  But there were and are converts as well. According to Jewish religious law, a convert to Judaism is just as much a Jew as one who is born to it.  It is similar to adoption in this sense - an adopted child is just as much your child as a child by birth.  

Most Christians don't quite understand the concept of a religion being passed down by birth, because in Christianity this doesn't happen.  Christianity has to be chosen, either by the individual or, in the case of a child, by the parent on behalf of the child.  

Both Judaism and Islam, however, pass their religion to the children at birth, though conversions happen also.  Thus you could have a Jew who does not practice Judaism; and her child will be a Jew by birth also, without ever practicing.  

Jews also lots of times don't understand that nobody is born a Christian, they assume Christians are born Christian just as Jews are born Jewish - unless they are converts of course.  

There are actually practicing Jews, isolated communities, in some parts of Africa; they are Black, but they practice Judaism the best they can and they have "Jewish DNA."  The best known of these are in Ethiopia, but there are others as well.  

You took a DNA test which is for entertainment value you got entertained......... so if you want to know who your ancestors were and where they came from you need to research and prove them from real written records............. and you will not get to know from entertainment DNA tests

Being Jewish is a religion not a race.

Religion doesn't show up in DNA tests.