It is correct to write four thirty for (4:30am/pm)? I do know that sometimes we will tell the time in that way but is it correct when it comes to writing? Or would it only be correct when we write "half past four"?
Technically, four thirty is correct, as is 4:30, but 4:30 is generally used as it is quicker to type, takes less space and is quicker and easier to read.
However, there is a fundamental difference. Four thirty is words so it has a pronunciation and a syllable count etc. 4:30 is ideogrammatic. I can read it aloud however I choose:
Half past four
Quatre heures et demie
So when the actual words are important, such as in reported speech (anywhere but especially in a witness statement) or in poetry (where rhyme and metre are important) and other similar situations, it may well be sensible to use the words.