hi. It's not "qui`l" nor "qui`elle". We clip the "i" of the word "qui" so it becomes qu' and then tack on "il" or "elle".So it's "qu'il" and "qu'elle". We do that because we don't like when a word finish with a vowel and the next one also start with a vowel.
You'd use "qu'il" and "qu'elle" in a verb tense called subjonctif. For example "it's necessary THAT HE buys some books" would be "il faut qu'il achète des livres".