Jazz Clue 1: Is it supposed to sound so awful to our ears when we play the one and five with the B and F in Here to Stay? In measure 7, the chord is B minor and the right hand is playing an F, so playing 1 and 5 in the left hand on B and F# doesn’t really sound good with an F.
There’s an important distinction in Here to Stay. Yes, Jazz Clue 1 on B is B and F# (the key to Jazz Clue 1 is that both notes are the same color except in the case of the Bs), but in Here to Stay, the B chord includes “-5”. That means flat 5, so in this instance the F# becomes F. Voila! Consonance.
Jazz Clue 1 played correctly will always sound consonant for any Maj, min, 7th, Maj7, and min7 chord and some others, but you need to watch for those rare adjustments of the 5th. That said, it won’t always sound very interesting. Jazz Clue 2 will be the salt on your musical mashed potatoes.