Script for the "Count it" button:

on mouseUp
  put 0 into total
  repeat with i = 1 to number of words of card field "text"
    if word 1 of card field "input" = word i of card field "text" then
      add 1 to total
    end if
  end repeat
  put "The word" && word 1 of card field "input" && "appears"  && total && "times in the text" into card field "results"
end mouseUp

Script for the "Reverse it" button:

on mouseUp
  put empty into card field "results"
  repeat with i = 1 to number of chars of word 1 of card field "input"
    put char i of word 1 of card field "input" before card field "results"
  end repeat
end mouseUp

Script for the "Palindrome?" button:

on mouseUp
  send mouseUp to button "Reverse it"
  if word 1 of card field "results" = word 1 of card field "input" then
    put "The word" && word 1 of card field "input" && "is a palindrome." into card field "results"
  else
    put "The word" && word 1 of card field "input" && "is not a palindrome." into card field "results"
  end if
end mouseUp