Bobby Fischer appeared on The Tonight Show starring Johnny Carson in 1978.
In November 1980, Joe Newton appeared on The Tonight Show starring Johnny Carson.
Buddy Rich appeared on The Tonight Show 43 times.
Laura Bush appeared eight times on The Tonight Show, once with Jimmy Fallon and the rest with Jay Leno.
The cast of The Don Lane Tonight Show - 1965 includes: Don Lane as Himself (1965-1969)
The cast of John Laws Tonight Show - 1968 includes: John Laws as Host (1968-1969)
The Tonight Show has aired 11,461 times as of this writing. It first aired in 1954 and is the longest-running talk show in history. Its hosts have been Steve Allen, Jack Paar, Johnny Carson, Jay Leno and, most recently, Jimmy Fallon.
I can find three appearances.
Yes, he appeared on The Tonight Show starring Johnny Carson four times but all his guest spots were prior to his presidency.
The Tonight Show
The Tonight Show was created on 1954-09-27.
Who was literally the first singer to appear on Steve Allen's Tonight Show has evidently been lost to broadcast history but I can find Eydie Gorme & Steve Lawrence appeared in the first year, 1953.
No. There is no monetary compensation for what is submitted to The Tonight Show.