'Unexpectedly' and 'unlikey' have different meanings. 'Unexpectedly' means that we did not expect it, it was a surprise for us. 'Unlikely' means that it probably won't happen. So, 'The Prime Minister is unlikely to endorse this view' means we do not think he is going to endorse it. It has a future meaning. 'The Prime Minister unexpectedly endorsed this view' means he did endorse it but it was a surprise. No-one thought that he would do this. It is in the past. It is possible to say 'The PM will unexpectedly endorse this view' but only in a very specific context of a reporter/person close to the PM who knows that the PM is going to endorse the view very soon (maybe to the press or in parliament that day) and we hadn't expected him to do this; it is a surprise - we thought he wouldn't endorse it.

"The Prime Minister is unexpectedly endorse this view." - this is incorrect. However, these are possible: "The Prime Minister unexpectedly endorsed this view." (past) "The Prime Minister is to unexpectedly endorse this view." (future; actually, even though this is grammatically correct, it makes no sense) It makes much more sense to use "unexpectedly" in a past context. You can use http://www.thefreedictionary.com/ or another online dictionary if you're not sure about the dictionary that you have.