How was this a response to Moshe's request "Keil Na, R'fa Na lah!"?
Rashi: Moshe asked Hashem to inform him whether He would answer him or not. 1 And Hashem replied in the affirmative, and that this is how He would cure her.
Seforno: Moshe asked Hashem whether, in order to spare Miriam the embarrassment, He would not cure her immediately without having to send her out of the Camp, to which Hashem replied that the embarrassment was an intrinsic part of her atonement. 2
Why did Hashem mention what Miriam's father would do?
Rashi and Targum Yonasan: Because, if her father would have been angry with her, he would have placed her in quarantine for seven days, 1 in which case, now that the Shechinah was angry with her, she ought to be quarantined for fourteen days. 2 And the reason that it was only seven was due to the principle 'Dayo Lavo min ha'Din Lih'yos ke'Nadun'. 3
What are the connotations of "Achar Te'asef"?
Rashi: Whenever the Torah uses the term 'Asifah' in connection with Metzora'im, it always has connotations of being gathered back into the camp.
Why did the Shechinah, the camp of Yisrael, the Aron and all of Yisrael delay seven days for Miriam to be cured?