I'm Portuguese and am going to Cyprus this summer for holidays. Can I use my driving licence as an ID document at the border?
NO - A driving licence isn't a travel document. You'll need a valid national identity card or passport.
I am German and am planning a trip to the UK. As it is not a member of the Schengen area, can I enter the UK with my German identity card or must I present my passport?
As an EU national, you can enter the UK, or indeed any other EU country, on presentation of your official German identity card. You do not need to present your passport.
In what circumstances can I, as an EU national, be refused entry into another EU country?
You can be refused entry into another European country if you present a serious threat to public policy, public security or public health. If this happens, you must be told why and how to appeal the decision.
What can I do if my right to enter another EU country is refused at the point of entry?
If your right to enter another EU country is refused, you should contact the embassy or consulate of your own country in the country you want to enter.