What did Yakov mean when he pointed out that the ewes and goats in Lavan's flocks did not lose their babies?
Seforno and Rashbam: He meant that, bearing in mind, his (Yakov's) total dedication when tending to his sheep, Lavan's suspicion that he had stolen from him was completely unfounded, considering the lengths to which he went to make sure that none of his ewes or goats miscarry.
Why did Yakov need to add add that he did not eat Lavan's rams?
Rashbam: He meant that he did not follow the custom of the shepherds of that time, who would slaughter and eat a lamb belonging to the owner from time to time.
Why did he mention specificaly "Eilim"? Does this mean that he ate Lavan's Kevasim?
Moshav Zekenim (from Bava Kama 65b): From here we see that even a newborn lamb is called "Ayil". 1
Even though a Drashah includes a Palgas (a sheep in its 13th month, for less than 13 months is not called Ayil), that is for Kodshim. Here we are discussing Chulin.
רש"י: איל בן יומו קרוי איל: לגבי קרבן רק בגיל 2 הוא נקרא איל?
גור אריה: בקרבנות יש חלוקה בין כבשים לאילים, ומזה לומדים שבעודו כבש אינו קרוי איל לגבי קרבנות כי 'איל' זה לשון חוזק, ורק בגיל 2 הוא מגיע למלֹא תוקפו. כאן אין חלוקה בין כבשים לאילים, ולכן גם בין יומו שמו איל כי הוא ממין חזק.