I won't try to answer question 2, or even 1b. But my definition of board strength is how strong pure BMU does against any strategy using any card or cards from the kingdom. The better pure BMU can do, the weaker the board.
There should always be something that's better than BMU... but sometimes not very much.
Three things: One, there are some boards that there's nothing better than BMU on (they're extremely extremely rare though). Two, and more important, there are a large number of strategies which are approximately 100% against BMU, and thus a lot of boards are going to top out your metric, but there's a lot of variation within board strength amongst these sets. Three, and this one is really tricky, there are going to be some boards which are weaker by your measure, but really stronger overall. What I have in mind is some way to set up a pin, very surely, but it's also going to be very surely slow. Of course, BMU is incredibly slow to end the game, so you could well get that pin set up in time usually, giving it a very good score on your metric. On the other hand, there may be some other board where a strategy is USUALLY very strong and fast, but sometimes not - think like chapel missing a reshuffle or something kills it, but something that is going to make it lose like 20% of the time - but this still might be usually better than the slow-but-surefire example. Something more reasonable is like a standard duke slog, which almost ALWAYS beats BMU, against an engine which is usually going to beat both but sometimes draws really badly and doesn't come together in time.
Having said all that, I do think this is a reasonably good rough proxy.
