THE GOAT USED FOR HEALING
What was so terrible about the sin of this Chasid that the Chachamim did not wish to visit him? Was he not doing it purely to heal himself?
Maharsha: It could be that he was not in mortal danger, so he should have refrained from doing that which the Chachamim had prohibited.
Ben Yehoyada: Despite not being in mortal danger, he permitted himself to do it since Chazal do not apply their decrees in cases of illness. However, the Chachamim viewed it as a sin since he was an important person and people might mistakenly learn to do this even without illness.
Meiri: Even though he was in mortal danger and almost all prohibitions are waived to save a person's life, if something was prohibited as a decree of Chazal because of concern for loss to others, one must be extremely strict with it, so he should not have used the goat.
What was the purpose of 'sitting down and looking into it' and how could they know if he had done other sins in private?
Kovetz Shiurim: It could be that they investigated him through Ruach Hakodesh. When visiting the sick, one must inspire and awaken them to Teshuva, to repent. To do so, they needed to know if he had any other sins for which to repent.
THE CHACHAMIM WENT TO A CELEBRATION
What is the meaning of Shavua ha'Ben and Yeshua ha'Ben?
Rashi: Shavua ha'Ben is a Bris Milah which takes place after a week (Shavua) has passed. A Yeshua ha'Ben is the banquet made for a Pidyon ha'Ben - a redemption of a firstborn, as Yeshua is translated as redemption.
Maharsha: Rashi explains that Shavua is the Milah itself, but he describes Yeshua as the banquet for a Pidyon ha'Ben. This implies that there is an obligation to make a Seudah only for a Pidyon ha'Ben, but not for a Bris Milah.
R' Tam: A Yeshua ha'Ben refers to a celebration for the birth of a boy, as the baby was saved (Yeshua) and escaped its mother's womb.
Mateh Moshe: The celebration (of Yeshua ha'Ben) mentioned by R' Tam is customarily done nowadays on the first Friday night after the baby is born. People come to the baby's home and taste something as a Seudas Mitzvah. (It must be a Seudas Mitzvah as Rav was a guest and he would only eat food from a Seudas Mitzvah - as stated in Chulin 95b.)