Jesus wasn't preaching to the multitudes in the Sermon on the Mount.
Matthew 5:1-2 And seeing the multitudes, he went up into a mountain, and when he was set down, his disciples came unto him. And opening his mouth, he taught them, saying:
Luke 6:20 And he, lifting up his eyes on his disciples, said: Blessed are ye poor, for yours is the kingdom of God.
In both places, it clearly says that Jesus was speaking to His disciples.
No it doesn't. Jesus had 24/7 access to His disciples, He didn't need a sermon to communicate to them. Further, we know that Jesus gave the sermon at least one other time at the Sermon on the Plain. No need to tell His disciples again. Many scholars believe that He gave His message to many different crowds and in the process created believers.
But they've heard it before and they either think Christ only spoke to His apostles on the Sermon on the Mount and no one else since the crowds most likely were out of earshot (not sure where they get this error from) or they think there were unbelievers among the crowds of His disciples (also false.)
They just make stuff up to accommodate their misconceptions.