How would they have travelled to Germany?

Potentially by train; the Luftwaffe wanted to get prisoners to their Dulag Luft interrogation centre at Oberusel rapidly to extract information so captured airmen would often travel under guard on civilian trains. Around the time of the Dunkirk evacuation, though, when large numbers of Allied troops had been taken prisoner (about 40,000 British) a pilot might well have been in the columns of prisoners forced to march hundreds of miles towards Germany followed by transport in terrible conditions on overcrowded trains or barges (though officers didn't have it quite as bad as other ranks). After interrogation at Dulag Luft RAF prisoners would be moved on to one of the Stalag Luft camps.

Would they likely have survived, and stayed put in the camp for the duration of the war?

Probably; relatively few British POWs died in captivity. There was some movement between camps as things were reorganised (e.g. Sergeant "Dixie" Deans was moved from Stalag Luft I to III to VI over the course of the war), and towards the end of the war extended marches as Allied and Soviet advances approached camps.

Were there any Allied rescue attempts, or many successful escapees?

Not rescue attempts, there wasn't a safe way of freeing prisoners deep in enemy territory (a raid on Amiens Prison in 1944, Operation Jericho, killed around 100 prisoners and few managed to escape for good). There were escape attempts, though not many successes; less than 30 out of 10,000 Air Force prisoners escaped and made it to Britain or neutral territory according to Aidan Crawley's Escape from Germany. The best chance was in evading capture in the first place, then escaping during transit to a prison camp, it was much more difficult once behind wire. To take a couple of examples of pilots captured around the time of Dunkirk Wing Commander Basil Embry was shot down on May 27th 1940, but slipped away from the column of prisoners as he was marched towards Germany and, over two months, managed to make his way across France to Gibraltar and back to Britain. Squadron Leader Roger Bushell was shot down and captured on May 23rd just before the Dunkirk evacuation; he later masterminded perhaps the most famous of attempts, The Great Escape, in which 76 airmen tunneled out of Stalag Luft III. Only three made it to freedom, though, 73 were recaptured, and 50 of those including Bushell himself were murdered.

Stories of camp life, particularly escape attempts and focused on Colditz Castle, Oflag IVC, became rather popular in 1950s Britain. The Colditz Myth : British and Commonwealth Prisoners of War in Nazi Germany by S. P. MacKenzie takes a wider view, pointing out that perhaps only 5% of POWs were really fanatical about escaping, though larger numbers were involved in supporting escape attempts. It's very accessible, and a good overview of the situation as a whole.