Why does the Torah write that the brothers saw that their father had died? Is it not obvious?
Rashi, from Bereishis Rabah 100:8: What the Torah means is that they saw signs that Yosef changed his attitude he had died. They tended to regularly eat by him, and, as long as Ya'akov was alive, Yosef would befriend them; but the moment he died, he kept his distance, and the brothers feared that he hated them 1 and intended to avenge what they had done to him, which in turn, explains why they approached him with the request stated in the following Pasuk.
Riva citing a Midrash, Ba'al ha'Turim: After burying Ya'akov, the brothers saw Yosef reciting a Berachah ('she'Asah Li Neis ba'Makom ha'Zeh'), which they misconstrued as his reliving the harm that they had done to him.
In fact however, he did that because if, until now, he sat at the head of the table because his father had placed him there; but now that his father as no longer alive, he felt that to do so would be a slight to Yehudah, who was king and to Reuven, who was the Bechor. On the other hand, it would be degrading for him, in his position as viceroy of Egypt, to sit below them (Sifsei Chachamim, citing Midrash Tanchuma).
What does "Lu Yistemeinu Yosef" mean?
Rashi, Targum Onkelos and Targum Yonasan: It means 'Perhaps Yosef will hate us. 1
Hadar Zekenim, Ba'al ha'Turim #1: 'If only Yosef would hate us (only) in his heart (and not take action against us). 2
Ba'al ha'Turim: May he return to us all the 'evil' that we did to him!' He became king of Egypt as a result of our having sold him.
Rav C. Fogel: 'If only Yosef would hate us [and try to harm us]' - when we did so to him, Hashem made him king!
רש"י: ומשמת יעקב לא קירבן: וכי יוסף הצדיק לא קרב את אחיו בכלל?
גור אריה: בימי אביו הוא קירבם יותר מהשיעור בכך שהם אכלו על שולחנו תמיד, ועכשיו לא קירבם כל כך.
גור אריה: אחרי שמת יעקב התחיל השיעבוד ויוסף חשש שאם הוא יקרב אותם- המצרים ילחמו בהם. 1
נראה שקירבת יוסף אליהם עלולה לגרום למצרים לחשוש ש"ונלחם בנו ועלה מן הארץ" ולכן יוסף התרחק מהם.
רש"י: ויש אולי לשון בקשה: למה רש"י נזקק לכך?
גור אריה: כדי לפרש ש"לוּ ישטמנו" פרושו 'שמא', הוכיח רש"י ש'אולי' ו'לוּ' מתפרשים לפעמים בלשון 'אם', וכך 'לוּ' יכול להתפרש 'שמא' כפי שמצאנו ב'אולי'.