In the story of Bar Hedya, Rava got the burnt end of the deal since he didn't pay Bar Hedya any money. At the end of the story, Rava said "I mochel you for everything except the daughter of Rav Chisda", who was his wife. Originally, I thought the reason he wasn't mochel for this was because it had to do with a death which was irreparable. But then I was bothered with two questions. Why then was he mochel Bar Hedya for his children that died, and for Abaye, who he also predicted would die and Rava would take over his position (I'm assuming that all of the predictions came true since "kol hachalomos holchim achar hapeh".) Why was his wife more important than his children and Abaye?
I found a Ben Yihoyada that says the reason he wasn't mochel for his wife was because he could only be mochel for something targeted at him. However, something targeted at his wife, he wasn't able to be mochel. However, that doesn't answer the other part of the question. Why was he then mochel for his children and Abaye?
As a side point, we know that both Abaye and Rava were mi'bnai Aili who were cursed with short lives. Rava, since he learned lived to forty. Abaye, since he learned and did chessed, lived until sixty. According to this curse, Rava should have lived later than Abaye. If you might try to answer that perhaps Abaye was older, that can't be because we find in Brochos, daf 48a that both Rava and Abaye were children in front of Raba at the same time. (Perhaps this prediction did not come true?)
Yehoash Orange, Brooklyn NY
The Sifsei Chachamim (cited in the Bi'urei ha'Daf at the back of Shas Lublin) explains that when Rava said that he was not Mochel the death of bas Rav Chisda, he meant to incorporate her children as well - not Abaye I assume, since he was an independent person with an independent family, who would or would not, be Mochel bar Hedya.
Personally, I understood that Rava was particularly fond of bas Rav Chisda, and that, as far as he was concerned, her death constituted the biggest loss for him (even more than that of his children).
Your other question is a good one - according to the Ein Ya'akov's version of the Gemara in Rosh Hashanah (18a), as cited by the Mesores ha'Shas. According to our version however, it is Abaye and Rabah (not Rava) who were descendents of Eli (see Rashi there).
As a matter of fact, in our version of the Ein Ya'akov, Rava appears in round parentheses, and Rabah, in square ones, in which case, there is not room for the Kashya altogether.
be'Virchas Kol Tuv
Concerning Abaye and Rava and how long they lived:
There's an essay by R Reuven Margolios in his Mehkarim bdarkei haTalmud vHidosav (p. 96) that touches on this topic.
He points out that there are sources for a girsa in berakhoth (48a) of Abaye and Rava bar Rav Hanan. So the gemarah doesn't indicate that Abbai and Rava were born around the same time.
Concerning the amended (see dikduke sofrim) girsa, Rabba and Abaye mBes Eli, R Margolios reports this problem: Rabba passed away in 631 (lShtaros, according to igeres R Shrira Gaon), Abaye in 649 and Rava in 663. So if Rabba was 40 and Abaye was 60 when they died, then Abaye was two years older than Rabba! But Abaye was orphaned and was brought up by Rabba his uncle. Therefore the girsa has to be "Abaye and Rava mBes Eli" (No one knows how old Rabba was when he died but it's clear that he lived to an old age even though he was also from Bes Eli.)
Rav Margolios also mentions that Rav Hai Gaon (in a tshuva) identifies 17 amoras who are called Rava. It's not always easy to identify which Rava is actually meant.
To summarize, Abaye died at the age of 60 and Rava lived 14 more years and died at the age of 40.
All the best,
Your final remark suggests that the original text "Abaye and Rava" remains intact and that Rava was from Beis Eli and died at 60.
But this is impossible, since Rava was not a Kohen as Tosfos proves.
Also, it is generally accepted that Stam Rava is Rava Brei d'Rav Yosef, the Chaver of Abaye.
be'Virchas Kol Tuv