The correct spellings are
--punctual
--punctuality
They both have the letter "C" in them.
"Punctuality" is the same as "punctual" with -ity added.
"Punctual" is an adjective.
"He is always punctual."
"Please be punctual."
The correct spelling is "diligent."
"He is a diligent person and punctual about arriving at work."
We form the adverb by adding -ly: "punctually."
You could say "I will arrive punctually at 4 o'clock."
"I will arrive at 4 o'clock on the dot" is more natural.
"Punctuality" is rare. It is a noun. it is the quality of being punctual.
"Punctuality is important in personal relationships."
"Three of her best qualities are cheerfulness, reliability, and punctuality."
Sometimes we form this kind of noun by adding "-ness", sometimes by adding "-ity."
The "punct-" root means "point" or "dot" and is found in a few other words such as
--"punctuation," . , : ; ? !
--"puncture," I have a flat tire because it was punctured.