How many instruments did the late producer George Martin know how to play, what were they, and which ones did he actually play in...?

Mainly keys; like piano or organ.

Most famously he played the piano solo on "In My Life". It was sped up which gave it that harpsichord-like sound.

He also played:

piano on "Misery",

piano on "P.S. I Love You"

celesta on "Baby It's You"

piano on "You've Really Got a Hold on Me"

Hammond organ on "I Wanna Be Your Man"

piano on "Not a Second Time"

piano on "Money (That's What I Want)"

piano on "Slow Down"

piano on "Matchbox"

piano on "A Hard Day's Night"

piano on "Tell Me Why"

piano on "No Reply"

piano on "Rock and Roll Music"

piano on "Kansas City/Hey, Hey, Hey, Hey"

piano on "What You're Doing"

piano on "You Like Me Too Much"

harmonium on "The Word"

harmonium on"If I Needed Someone"

sang in the chorus on "Yellow Submarine"

piano on "Good Day Sunshine"

piano on "Tomorrow Never Knows"

organ on "Sgt. Pepper's Lonely Hearts Club Band"

Hammond organ on "With a Little Help from My Friends"

piano, pianet, and virginal on "Getting Better"

harpsichord on "Fixing a Hole"

piano, harmonium, Lowrey organ, glockenspiel, tape loops, and Hammond organ on "Being for the Benefit of Mr. Kite!"

piano on "Lovely Rita"

harmonium for the final 'endless' chord on "A Day in the Life"

piano on "Penny Lane"

piano on "All You Need Is Love"

piano on "Back in the U.S.S.R."

honky-tonk piano on "Rocky Racoon"

harmonium on "Cry Baby Cry"

spoken vocals on "Revolution 9"

celesta on "Good Night"

organ on "Maxwell's Silver Hammer"

Baldwin electric spinet on "Because"

Lowrey organ on "Sun King"

Hammond organ on a version of "Across the Universe"

maracas on "Dig It"

Not to mentions a lot of orchestral composition and conducting. Such as "Eleanor Rigby", "She's Leaving Home", "Strawberry Fields Forever", the "Yellow Submarine" film soundtrack, and many more.