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In English, the word "a" has two forms: "a" and "an", determined by the sound that the following word begins with. "An apple", but "a pear". So it is in Hawaiian. "Ka" has two forms: "ke" before words starting with "k", "e", "a", or "o" (and a scattered few other words), "ka" elsewhere.
The usual mnemonic is "ke ao" (the cloud). It contains all the letters, makes sense as a phrase, and is an application of the rule.
Note that a word that starts with an ‘okina does not fit the "ke ao" rule.
No, it shouldn't. «Ka» changes to «ke» before words starting with k, e, a, o.