Can I bring nail clippers, scotch tape, and disposable razors on a plane?

Im leaving for Europe on Tuesday night...I was just wondering (since I will be bringing my suitcase on the plane with me) can I bring nail clippers? My sister said they were not allowed in carry-on luggage, but I want to know for sure. What about scotch tape, it has that little tiny razor to cut the tape, is that considered a weapon? What about disposable razors for shaving when I get to Europe? There is no info on these items on the airline website.