1) The best explanation for Shakespeare is that Elizabethan plays were a relatively new phenomenon, and that he was retelling stories from maybe 50-100 years prior that have since been lost (thus he may have been a clever "hack" who was lucky to have been among first to have plays published and preserved). When you read the 1350ish "Decameron", you realize that many stories had been around for hundreds of years and retold.

2) Robin Hood appears in "Piers Plowman" 1377. I believe the joke was that during festivals, a woman would go out into the forest, get impregnated, and the father was said to be "Robin Hood", the mythical forest bandit. There may have been people that called themselves "Robin Hood" also, and a quasi historical basis.

3) I'm not sure about Swiss legends, maybe those who know don't Tell?

4) I have read several books about British History, consensus is kind of "If Venerable Bede didn't write about it in 730, it may not have happened" (certainly if Arthur's exploits were all true, Bede would've had more to say about them). We visited Glastonbury where King Arthur and Guinevere's graves were supposedly found in 1100s. I guess contemporary Geoffrey of Monmouth may have been a fictional "historical romance writer". As you say, closest thing might be Lucius Arturious Castus. Until proved otherwise, I'm believing the Monty Python version.