Priam kissing the hands of Achilles
1. My opinion of Achilles has not really changed as a result of his reception of Priam. I still think he's a selfish, egotistical, jerk, only now I see that Achilles does indeed have a soft spot. When Priam asks for pity he asks Achilles to remember Peleus, Achilles father. Priam and Achilles cry for their losses, Achilles for Patroclus and Priam for Hector. Achilles shows Priam hospitality to Priam by giving Priam food and a bed; he also has Hector's body cleaned and anointed before letting Priam see it. Besides returning the body of Hector to Priam Achilles also agrees to hold off from fighting for twelve days or as long as the funeral process would take.
2. I feel more sympathetic towards Priam, because he has to beg Achilles for his son's body back and kiss Achilles' hands, the hands by which the spear that killed his son was thrust into Hector's throat, killing him.
3. Achilles' human emotions are shown with his episode with Priam. He shows compassion towards Priam and love for his father. He shows kindness and concern towards Priam by providing Priam with food and a bed, also he's concerned for Priam's safety if Priam makes him mad.
4. I know that the Greek's view fate as something that can't be changed; they're born with it and they just have to accept it. That's all I know though, I'm not sure what the passage where Zeus is talking about jars means.
7. I believe that "The Illiad" does have a theme that relates to life today. One theme is that even in war against your worst enemy, the utmost respect should be shown toward the dead. By returning Hector's body to Priam, Achilles is showing great respect toward not necessarily Hector, but Priam. I think this still applies today, with prisoners of war. Prisoners of war should be returned, dead or alive to their country, preferably alive, but you can't get everything you want.