Yes, the British had a strong enough navy to ensure that the Germans could not gain control of the seas. In fact, Admiral Raeder of the Kreigsmarine had said at the beginning of the war that all the vastly outnumbered German navy could do was show that "they knew how to die gallantly". Given those circumstances, I think it can fairly be said that both the British and the German navies fought exceedingly well. They were worthy adversaries.

The British successfully fended off the German air attacks in 1940 adn prevented an invasion of the UK. I believe they would have been able to continue preventing it indefinitely. This is not to say, however, that they could have ever mounted a successful counterinvasion of western Europe...not without American assistance.

To win a battle is not to win a war. The British won a number of battles. So did the Germans. I don't think that either one of them would have been able to decisively defeat the other if America had stayed out of the European war.

Rommel could definitely have won in Africa if Hitler had arranged to supply him properly in the early stages of the campaign...but Hitler was not all that interested in doing so until it was far too late. That may have been Hitler's 2nd biggest mistake (after the invasion of Russia).