Do the sources describe removing (nikkur/taber) the gid hanasheh (sciatic nerve) and chelev (forbidden fats) from the Pashcal Offering when it was roasted whole? If not, would cooking the sciatic nerve and chelev render the hindquarters or the whole animal non-kosher?
How does one get the chelev out of the insides of the carcass without breaking bones?
(The process is described here): .
This is a Korban, so the Chelev was burned on the Mizbeach.
Regarding the Gid haNasheh, there is a famous disagreement between the Rambam and the Raavad (Korban Pesach 10:11):
כשאדם אוכל את הפסח חותך הבשר ואוכל וחותך העצמות מן הפרק ומפרקן אם רצה. וכשיגיע לגיד הנשה מוציאו ומניחו עם שאר הגידים והעצמות והקרומות שיוצאין בשעת אכילה. שאין מנקין אותו כשאר הבשר ואין מחתכין אותו אלא צולין אותו שלם.
א"א בחיי ראשי אין איסור גדול מזה שיצלה הפסח עם גיד הנשה ועם שמנו ועם תרבא דתותי מתנא ועם קרומות שבראש ואם אזכה ואוכל פסח ויביא לפני כזה הייתי חובטו בקרקע לפניו:
When a person eats the Pesach he cuts the meat and eats, and cuts the bones at the joints and splits them if he wants. And when he arrives at the Gid haNasheh he removes it and places it with the other sinews, bones and membranes which are removed while eating. For we don't clean [the Pesach] like ordinary meat and we don't cut it, rather we roast it whole.
Said [Ra]A[VaD]: In the life of my head there is no greater prohibition than this that one would roast the Pesach with the Gid haNasheh and its [surrounding fats and other prohibited membranes], and if I merit and eat a Pesach and he brings before me like that I would throw it on the ground in front of him. (my translation)
As for why the Rambam holds it's ok, see the commentaries there for various possibilities, but the simplest answer is the Gid haNasheh doesn't have any flavor so it can't prohibit the surrounding meat and the fats around the Gid haNasheh are only prohibited as a custom.
