"Gleeful" is not a very nice word to use of people. This is what glee means , "Great delight, especially from one’s own good fortune or another’s misfortune". (Oxford Dictionaries) Often when learners use "glee" all they need is "delight". So be more ready to use "happy" and "delighted", and less ready to use "gleeful". "Gleeful" may gave become more neutral over the years - "exuberantly or triumphantly joyful" - but it is still difficult to use well or even correctly.

The grammar is right in the first one, but it sounds awkward. Gleeful isn't quite the right word. I'd write. His smile showed he was gleeful. The smile itself isn't gleeful. The person is. The second needs gleefully. The third is fine.

The first and third examples are correct. You should also use "gleefully" in the second one.