The correct answer is Option 1: She applauded her saying that she had done well.

The given sentence is in direct speech: "She said, “Bravo! You have done well.”" To convert it into indirect speech, we need to make several changes. First, the reporting verb ("said") needs to be replaced with a verb that reflects the meaning of "Bravo!" which is an expression of enthusiastic approval or applause. "Applauded" is the most suitable replacement. Second, the tense of the reported clause ("You have done well") needs to be shifted back one step to maintain consistency with the reporting verb’s past tense. This changes "have done" to "had done" to reflect the past perfect tense, indicating an action completed before the applauding. Third, the pronoun "You" needs to be changed to reflect the intended recipient of the applause, implied by the original sentence. The pronoun change to "her" depends on the context and the prior sentence, which is missing. Option 1 correctly accounts for all these adjustments.

Let's look at why the other options are incorrect:

• Option 2: "She told her saying that she had done well." - "Told" doesn't accurately convey the enthusiastic approval implied by "Bravo!".
• Option 3: "She applauded her saying that she did well." - The tense of the reported clause is incorrect. It should be past perfect ("had done") to reflect an action completed before the time of the reporting verb.
• Option 4: "She applauded her saying that she has done well." - The tense of the reported clause is again incorrect. It should be past perfect to maintain temporal consistency.

Therefore, only Option 1 accurately reflects the meaning and grammatical requirements of changing the given sentence from direct to indirect speech.